Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2475

Search results for: line graphs

2475 Improvement a Lower Bound of Energy for Some Family of Graphs, Related to Determinant of Adjacency Matrix

Authors: Saieed Akbari, Yousef Bagheri, Amir Hossein Ghodrati, Sima Saadat Akhtar

Abstract:

Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G.

Keywords: eigenvalues, energy, line graphs, matching number

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2474 Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs

Authors: Swapnil Gupta, C. Pandu Rangan

Abstract:

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: uniquely restricted matching, interval graph, matching, induced matching, witness counting

Procedia PDF Downloads 292
2473 Semirings of Graphs: An Approach Towards the Algebra of Graphs

Authors: Gete Umbrey, Saifur Rahman

Abstract:

Graphs are found to be most capable in computing, and its abstract structures have been applied in some specific computations and algorithms like in phase encoding controller, processor microcontroller, and synthesis of a CMOS switching network, etc. Being motivated by these works, we develop an independent approach to study semiring structures and various properties by defining the binary operations which in fact, seems analogous to an existing definition in some sense but with a different approach. This work emphasizes specifically on the construction of semigroup and semiring structures on the set of undirected graphs, and their properties are investigated therein. It is expected that the investigation done here may have some interesting applications in theoretical computer science, networking and decision making, and also on joining of two network systems.

Keywords: graphs, join and union of graphs, semiring, weighted graphs

Procedia PDF Downloads 65
2472 Extremal Laplacian Energy of Threshold Graphs

Authors: Seyed Ahmad Mojallal

Abstract:

Let G be a connected threshold graph of order n with m edges and trace T. In this talk we give a lower bound on Laplacian energy in terms of n, m, and T of G. From this we determine the threshold graphs with the first four minimal Laplacian energies. We also list the first 20 minimal Laplacian energies among threshold graphs. Let σ=σ(G) be the number of Laplacian eigenvalues greater than or equal to average degree of graph G. Using this concept, we obtain the threshold graphs with the largest and the second largest Laplacian energies.

Keywords: Laplacian eigenvalues, Laplacian energy, threshold graphs, extremal graphs

Procedia PDF Downloads 306
2471 An Improved Method to Compute Sparse Graphs for Traveling Salesman Problem

Authors: Y. Wang

Abstract:

The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CNmaxn2) where C is the iterations, Nmax is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem

Procedia PDF Downloads 138
2470 2D Structured Non-Cyclic Fuzzy Graphs

Authors: T. Pathinathan, M. Peter

Abstract:

Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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2469 Building 1-Well-Covered Graphs by Corona, Join, and Rooted Product of Graphs

Authors: Vadim E. Levit, Eugen Mandrescu

Abstract:

A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered.

Keywords: maximum independent set, corona, concatenation, join, well-covered graph

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2468 Reductions of Control Flow Graphs

Authors: Robert Gold

Abstract:

Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modelled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyse the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: control flow graph, graph reduction, software engineering, software applications

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2467 Nullity of t-Tupple Graphs

Authors: Khidir R. Sharaf, Didar A. Ali

Abstract:

The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: graph theory, graph spectra, nullity of graphs, statistic

Procedia PDF Downloads 157
2466 Study of Hydrocarbons Metering Issues in Algerian Fields under the New Law Context

Authors: A. Hadjadj, S. Maamir

Abstract:

Since the advent of the law 86/14 concerning the
exploitation of the national territory by foreign companies in
partnership with the Algerian oil and gas company, the problem of
hydrocarbons metering in the sharing production come out.
More generally, good management counting hydrocarbons can
provide data on the production wells, the field and the reservoir for
medium and long term planning, particularly in the context of the
management and field development.
In this work, we are interested in the transactional metering which
is a very delicate and crucial period in the current context of the new
hydrocarbon’s law characterized by assets system between the
various activities of Sonatrach and its foreign partners.
After a state of the art on hydrocarbons metering devices in
Algeria and elsewhere, we will decline the advantages and
disadvantages of each system, and then we describe the problem to
try to reach an optimal solution.

Keywords: transactional metering, flowmeter orifice, heat flow, Sonatrach

Procedia PDF Downloads 259
2465 On the Zeros of the Degree Polynomial of a Graph

Authors: S. R. Nayaka, Putta Swamy

Abstract:

Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

Procedia PDF Downloads 157
2464 Jordan Curves in the Digital Plane with Respect to the Connectednesses given by Certain Adjacency Graphs

Authors: Josef Slapal

Abstract:

Digital images are approximations of real ones and, therefore, to be able to study them, we need the digital plane Z2 to be equipped with a convenient structure that behaves analogously to the Euclidean topology on the real plane. In particular, it is required that such a structure allows for a digital analogue of the Jordan curve theorem. We introduce certain adjacency graphs on the digital plane and prove digital Jordan curves for them thus showing that the graphs provide convenient structures on Z2 for the study and processing of digital images. Further convenient structures including the wellknown Khalimsky and Marcus-Wyse adjacency graphs may be obtained as quotients of the graphs introduced. Since digital Jordan curves represent borders of objects in digital images, the adjacency graphs discussed may be used as background structures on the digital plane for solving the problems of digital image processing that are closely related to borders like border detection, contour filling, pattern recognition, thinning, etc.

Keywords: digital plane, adjacency graph, Jordan curve, quotient adjacency

Procedia PDF Downloads 289
2463 On Chvátal’s Conjecture for the Hamiltonicity of 1-Tough Graphs and Their Complements

Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

Abstract:

In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

Procedia PDF Downloads 174
2462 First-Year Undergraduate Students' Dilemma with Kinematics Graphs

Authors: Itumeleng Phage

Abstract:

Students’ comprehension of graphs may be affected by the characteristics of the discipline in which the graph is used, the type of the task as well as the background of the students who are the readers or interpreters of the graph. This research study investigated these aspects of the graph comprehension of 152 first-year undergraduate physics students by comparing their responses to corresponding tasks in the mathematics and physics disciplines. The discipline characteristics were analysed for four task-related constructs namely coordinates, representations, area and slope. Students’ responses to corresponding visual decoding and judgement tasks set in mathematics and kinematics contexts were statistically compared. The effects of the participants’ gender, year of school completion and study course were determined as reader characteristics. The results of the empirical study indicated that participants generally transferred their mathematics knowledge on coordinates and representation of straight line graphs to the physics contexts, but not in the cases of parabolic and hyperbolic functions or area under graphs. Insufficient understanding of the slope concept contributed to weak performances on this construct in both mathematics and physics contexts. Discipline characteristics seem to play a vital role in students’ understanding, while reader characteristics had insignificant to medium effects on their responses.

Keywords: kinematics graph, discipline characteristics, constructs, coordinates, representations, area and slope

Procedia PDF Downloads 190
2461 Influence of the Line Parameters in Transmission Line Fault Location

Authors: Marian Dragomir, Alin Dragomir

Abstract:

In the paper, two fault location algorithms are presented for transmission lines which use the line parameters to estimate the distance to the fault. The first algorithm uses only the measurements from one end of the line and the positive and zero sequence parameters of the line, while the second one uses the measurements from both ends of the line and only the positive sequence parameters of the line. The algorithms were tested using a transmission grid transposed in MATLAB. In a first stage it was established a fault location base line, where the algorithms mentioned above estimate the fault locations using the exact line parameters. After that, the positive and zero sequence resistance and reactance of the line were calculated again for different ground resistivity values and then the fault locations were estimated again in order to compare the results with the base line results. The results show that the algorithm which uses the zero sequence impedance of the line is the most sensitive to the line parameters modifications. The other algorithm is less sensitive to the line parameters modification.

Keywords: estimation algorithms, fault location, line parameters, simulation tool

Procedia PDF Downloads 256
2460 Upper Bounds on the Paired Domination Number of Cubic Graphs

Authors: Bin Sheng, Changhong Lu

Abstract:

Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by γₚᵣ(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γₚᵣ(G) ≤ 4n/7 holds for every graph G with δ(G) ≥ 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

Keywords: paired dominating set, upper bound, cubic graphs, weight function

Procedia PDF Downloads 74
2459 Graph Similarity: Algebraic Model and Its Application to Nonuniform Signal Processing

Authors: Nileshkumar Vishnav, Aditya Tatu

Abstract:

A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

Procedia PDF Downloads 264
2458 Hosoya Polynomials of Zero-Divisor Graphs

Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim

Abstract:

The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: Hosoya polynomial, wiener index, Hyper-Wiener index, zero-divisor graphs

Procedia PDF Downloads 438
2457 The K-Distance Neighborhood Polynomial of a Graph

Authors: Soner Nandappa D., Ahmed Mohammed Naji

Abstract:

In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.

Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials

Procedia PDF Downloads 334
2456 Analysis and Improvement of Efficiency for Food Processing Assembly Lines

Authors: Mehmet Savsar

Abstract:

Several factors affect productivity of Food Processing Assembly Lines (FPAL). Engineers and line managers usually do not recognize some of these factors and underutilize their production/assembly lines. In this paper, a special food processing assembly line is studied in detail, and procedures are presented to illustrate how productivity and efficiency of such lines can be increased. The assembly line considered produces ten different types of freshly prepared salads on the same line, which is called mixed model assembly line. Problems causing delays and inefficiencies on the line are identified. Line balancing and related tools are used to increase line efficiency and minimize balance delays. The procedure and the approach utilized in this paper can be useful for the operation managers and industrial engineers dealing with similar assembly lines in food processing industry.

Keywords: assembly lines, line balancing, production efficiency, bottleneck

Procedia PDF Downloads 297
2455 The Analysis of Split Graphs in Social Networks Based on the k-Cardinality Assignment Problem

Authors: Ivan Belik

Abstract:

In terms of social networks split graphs correspond to the variety of interpersonal and intergroup relations. In this paper we analyse the interaction between the cliques (socially strong and trusty groups) and the independent sets (fragmented and non-connected groups of people) as the basic components of any split graph. Based on the Semi-Lagrangean relaxation for the k-cardinality assignment problem we show the way of how to minimize the socially risky interactions between the cliques and the independent sets within the social network.

Keywords: cliques, independent sets, k-cardinality assignment, social networks, split graphs

Procedia PDF Downloads 224
2454 An Assembly Line Designing Study for a Refrigeration Industry

Authors: Emin Gundogar, Burak Erkayman, Aysegul Yilmaz, Nusret Sazak

Abstract:

When considering current competition conditions on the world, satisfying customer demands on time has become an important factor that enables the firms take a step further. Therefore, production process must be completed faster to take the competitive advantage. A balanced assembly line is the one of most important factors affecting the speed of production lines. The aim of this study is to build an assembly line to balance the assembly line and to simulate it for different scenarios through a refrigerator factory. The times of the operations is analyzed and grouped by the priorities. First, a Kilbridge & Wester heuristics is put to the model then a simulation approach is implemented to the model and the differences are observed.

Keywords: assembly line design, assembly line balancing, simulation modelling, refrigeration industry

Procedia PDF Downloads 355
2453 Framework Study on Single Assembly Line to Improve Productivity with Six Sigma and Line Balancing Approach

Authors: Inaki Maulida Hakim, T. Yuri M. Zagloel, Astari Wulandari

Abstract:

Six sigma is a framework that is used to identify inefficiency so that the cause of inefficiency will be known and right improvement to overcome cause of inefficiency can be conducted. This paper presents result of implementing six sigma to improve piston assembly line in Manufacturing Laboratory, Universitas Indonesia. Six sigma framework will be used to analyze the significant factor of inefficiency that needs to be improved which causes bottleneck in assembly line. After analysis based on six sigma framework conducted, line balancing method was chosen for improvement to overcome causative factor of inefficiency which is differences time between workstation that causes bottleneck in assembly line. Then after line balancing conducted in piston assembly line, the result is increase in efficiency. Efficiency is shown in the decreasing of Defects per Million Opportunities (DPMO) from 900,000 to 700,000, the increasing of level of labor productivity from 0.0041 to 0.00742, the decreasing of idle time from 121.3 seconds to 12.1 seconds, and the increasing of output, which is from 1 piston in 5 minutes become 3 pistons in 5 minutes.

Keywords: assembly line, line balancing, productivity, six sigma

Procedia PDF Downloads 217
2452 Analysis of Exponential Nonuniform Transmission Line Parameters

Authors: Mounir Belattar

Abstract:

In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

Procedia PDF Downloads 336
2451 Enhancement of the Performance of Al-Qatraneh 33-kV Transmission Line Using STATCOM: A Case Study

Authors: Ali Hamad, Ibrahim Al-Drous, Saleh Al-Jufout

Abstract:

This paper presents a case study of using STATCOM to enhance the performance of Al-Qatraneh 33-kV transmission line. The location of the STATCOM was identified maintaining minimum voltage drops at the 110 load nodes. The transmission line and the 110 load nodes have been modeled by MATLAB/Simulink. The suggested STATCOM and its location will increase the transmission capability of this transmission line and overcome the overload expected in the year 2020. The annual percentage loading rise has been considered as 14%. A graphical representation of the line voltages and the voltage drops at different load nodes has been illustrated.

Keywords: FACTS, MATLAB, STATCOM, transmission line, voltage drop

Procedia PDF Downloads 318
2450 Principal Component Analysis Applied to the Electric Power Systems – Practical Guide; Practical Guide for Algorithms

Authors: John Morales, Eduardo Orduña

Abstract:

Currently the Principal Component Analysis (PCA) theory has been used to develop algorithms regarding to Electric Power Systems (EPS). In this context, this paper presents a practical tutorial of this technique detailed their concept, on-line and off-line mathematical foundations, which are necessary and desirables in EPS algorithms. Thus, features of their eigenvectors which are very useful to real-time process are explained, showing how it is possible to select these parameters through a direct optimization. On the other hand, in this work in order to show the application of PCA to off-line and on-line signals, an example step to step using Matlab commands is presented. Finally, a list of different approaches using PCA is presented, and some works which could be analyzed using this tutorial are presented.

Keywords: practical guide; on-line; off-line, algorithms, faults

Procedia PDF Downloads 473
2449 Transmission Line Inspection Using Drones

Authors: Jae Kyung Lee, Joon Young Park

Abstract:

Maintenance on power transmission lines requires a lot of works. Sometimes they should be maintained on live-line environment with high altitude. Therefore, there always exist risks of falling from height and electric shock. To decline those risks, drones are recently applying on the electric power industry. This paper presents new operational technology while inspecting power transmission line. This paper also describes a technique for creating a flight path of a drone for transmission line inspection and a technique for controlling the drones of different types. Its technical and economical feasibilities have confirmed through experiments.

Keywords: drones, transmission line, inspection, control system

Procedia PDF Downloads 256
2448 Location-Domination on Join of Two Graphs and Their Complements

Authors: Analen Malnegro, Gina Malacas

Abstract:

Dominating sets and related topics have been studied extensively in the past few decades. A dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Some problems involving detection devices can be modeled with graphs. Finding the minimum number of devices needed according to the type of devices and the necessity of locating the object gives rise to locating-dominating sets. A subset S of vertices of a graph G is called locating-dominating set, LD-set for short, if it is a dominating set and if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. The location-domination number λ(G) is the minimum cardinality of an LD-set for G. The complement of a graph G is a graph Ḡ on same vertices such that two distinct vertices of Ḡ are adjacent if and only if they are not adjacent in G. An LD-set of a graph G is global if it is an LD-set of both G and its complement Ḡ. The global location-domination number λg(G) is defined as the minimum cardinality of a global LD-set of G. In this paper, global LD-sets on the join of two graphs are characterized. Global location-domination numbers of these graphs are also determined.

Keywords: dominating set, global locating-dominating set, global location-domination number, locating-dominating set, location-domination number

Procedia PDF Downloads 111
2447 Some Codes for Variants in Graphs

Authors: Sofia Ait Bouazza

Abstract:

We consider the problem of finding a minimum identifying code in a graph. This problem was initially introduced in 1998 and has been since fundamentally connected to a wide range of applications (fault diagnosis, location detection …). Suppose we have a building into which we need to place fire alarms. Suppose each alarm is designed so that it can detect any fire that starts either in the room in which it is located or in any room that shares a doorway with the room. We want to detect any fire that may occur or use the alarms which are sounding to not only to not only detect any fire but be able to tell exactly where the fire is located in the building. For reasons of cost, we want to use as few alarms as necessary. The first problem involves finding a minimum domination set of a graph. If the alarms are three state alarms capable of distinguishing between a fire in the same room as the alarm and a fire in an adjacent room, we are trying to find a minimum locating domination set. If the alarms are two state alarms that can only sound if there is a fire somewhere nearby, we are looking for a differentiating domination set of a graph. These three areas are the subject of much active research; we primarily focus on the third problem. An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most r≥1 from x. When only vertices out of the code are asked to be identified, we get the related concept of a locating dominating set. The problem of finding an identifying code (resp a locating dominating code) of minimum size is a NP-hard problem, even when the input graph belongs to a number of specific graph classes. Therefore, we study this problem in some restricted classes of undirected graphs like split graph, line graph and path in a directed graph. Then we present some results on the identifying code by giving an exact value of upper total locating domination and a total 2-identifying code in directed and undirected graph. Moreover we determine exact values of locating dominating code and edge identifying code of thin headless spider and locating dominating code of complete suns.

Keywords: identiying codes, locating dominating set, split graphs, thin headless spider

Procedia PDF Downloads 389
2446 Flexible Mixed Model Assembly Line Design: A Strategy to Respond for Demand Uncertainty at Automotive Part Manufacturer in Indonesia

Authors: T. Yuri, M. Zagloel, Inaki M. Hakim, Tegu Bintang Nugraha

Abstract:

In an era of customer centricity, automotive parts manufacturer in Indonesia must be able to keep up with the uncertainty and fluctuation of consumer demand. Flexible Manufacturing System (FMS) is a strategy to react to predicted and unpredicted changes of demand in automotive industry. This research is about flexible mixed model assembly line design through Value Stream Mapping (VSM) and Line Balancing in mixed model assembly line prior to simulation. It uses value stream mapping to identify and reduce waste while finding the best position to add or reduce manpower. Line balancing is conducted to minimize or maximize production rate while increasing assembly line productivity and efficiency. Results of this research is a recommendation of standard work combination for specifics demand scenario which can enhance assembly line efficiency and productivity.

Keywords: automotive industry, demand uncertainty, flexible assembly system, line balancing, value stream mapping

Procedia PDF Downloads 220