**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**903

# Search results for: random graph

##### 903 The Giant Component in a Random Subgraph of a Weak Expander

**Authors:**
Yilun Shang

**Abstract:**

In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

**Keywords:**
subgraph,
expander,
random graph,
giant component,
percolation.

##### 902 Syntactic Recognition of Distorted Patterns

**Authors:**
Marek Skomorowski

**Abstract:**

**Keywords:**
Syntactic pattern recognition,
Distorted patterns,
Random graphs,
Graph grammars.

##### 901 Topological Properties of an Exponential Random Geometric Graph Process

**Authors:**
Yilun Shang

**Abstract:**

**Keywords:**
random geometric graph,
autoregressive process,
degree,
connectivity,
Markovian,
wireless network.

##### 900 Protein Graph Partitioning by Mutually Maximization of cycle-distributions

**Authors:**
Frank Emmert Streib

**Abstract:**

**Keywords:**
Graph partitioning,
unweighted graph,
protein domains.

##### 899 Efficient Filtering of Graph Based Data Using Graph Partitioning

**Authors:**
Nileshkumar Vaishnav,
Aditya Tatu

**Abstract:**

**Keywords:**
Graph signal processing,
graph partitioning,
inverse
filtering on graphs,
algebraic signal processing.

##### 898 Using Spectral Vectors and M-Tree for Graph Clustering and Searching in Graph Databases of Protein Structures

**Authors:**
Do Phuc,
Nguyen Thi Kim Phung

**Abstract:**

**Keywords:**
Eigenvalues,
m-tree,
graph database,
protein
structure,
spectra graph theory.

##### 897 A Neighborhood Condition for Fractional k-deleted Graphs

**Authors:**
Sizhong Zhou,
Hongxia Liu

**Abstract:**

Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.

**Keywords:**
Graph,
minimum degree,
neighborhood union,
fractional k-factor,
fractional k-deleted graph.

##### 896 The Extremal Graph with the Largest Merrifield-Simmons Index of (n, n + 2)-graphs

**Authors:**
M. S. Haghighat,
A. Dolati,
M. Tabari,
E. Mohseni

**Abstract:**

The Merrifield-Simmons index of a graph G is defined as the total number of its independent sets. A (n, n + 2)-graph is a connected simple graph with n vertices and n + 2 edges. In this paper we characterize the (n, n+2)-graph with the largest Merrifield- Simmons index. We show that its Merrifield-Simmons index i.e. the upper bound of the Merrifield-Simmons index of the (n, n+2)-graphs is 9 × 2n-5 +1 for n ≥ 5.

**Keywords:**
Merrifield-Simmons index,
(n,
n+2)-graph.

##### 895 A Study about the Distribution of the Spanning Ratios of Yao Graphs

**Authors:**
Maryam Hsaini,
Mostafa Nouri-Baygi

**Abstract:**

A critical problem in wireless sensor networks is limited battery and memory of nodes. Therefore, each node in the network could maintain only a subset of its neighbors to communicate with. This will increase the battery usage in the network because each packet should take more hops to reach its destination. In order to tackle these problems, spanner graphs are defined. Since each node has a small degree in a spanner graph and the distance in the graph is not much greater than its actual geographical distance, spanner graphs are suitable candidates to be used for the topology of a wireless sensor network. In this paper, we study Yao graphs and their behavior for a randomly selected set of points. We generate several random point sets and compare the properties of their Yao graphs with the complete graph. Based on our data sets, we obtain several charts demonstrating how Yao graphs behave for a set of randomly chosen point set. As the results show, the stretch factor of a Yao graph follows a normal distribution. Furthermore, the stretch factor is in average far less than the worst case stretch factor proved for Yao graphs in previous results. Furthermore, we use Yao graph for a realistic point set and study its stretch factor in real world.

**Keywords:**
Wireless sensor network,
spanner graph,
Yao Graph.

##### 894 N-Sun Decomposition of Complete, Complete Bipartite and Some Harary Graphs

**Authors:**
R. Anitha,
R. S. Lekshmi

**Abstract:**

**Keywords:**
Decomposition,
Hamilton cycle,
n-sun graph,
perfect matching,
spanning tree.

##### 893 The Diameter of an Interval Graph is Twice of its Radius

**Authors:**
Tarasankar Pramanik,
Sukumar Mondal,
Madhumangal Pal

**Abstract:**

In an interval graph G = (V,E) the distance between two vertices u, v is de£ned as the smallest number of edges in a path joining u and v. The eccentricity of a vertex v is the maximum among distances from all other vertices of V . The diameter (δ) and radius (ρ) of the graph G is respectively the maximum and minimum among all the eccentricities of G. The center of the graph G is the set C(G) of vertices with eccentricity ρ. In this context our aim is to establish the relation ρ = δ 2 for an interval graph and to determine the center of it.

**Keywords:**
Interval graph,
interval tree,
radius,
center.

##### 892 Completion Number of a Graph

**Authors:**
Sudhakar G

**Abstract:**

In this paper a new concept of partial complement of a graph G is introduced and using the same a new graph parameter, called completion number of a graph G, denoted by c(G) is defined. Some basic properties of graph parameter, completion number, are studied and upperbounds for completion number of classes of graphs are obtained , the paper includes the characterization also.

**Keywords:**
Completion Number,
Maximum Independent subset,
Partial complements,
Partial self complementary

##### 891 On Fractional (k,m)-Deleted Graphs with Constrains Conditions

**Authors:**
Sizhong Zhou,
Hongxia Liu

**Abstract:**

Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

**Keywords:**
Graph,
degree condition,
fractional k-factor,
fractional (k,
m)-deleted graph.

##### 890 Metric Dimension on Line Graph of Honeycomb Networks

**Authors:**
M. Hussain,
Aqsa Farooq

**Abstract:**

**Keywords:**
Resolving set,
metric dimension,
honeycomb network,
line graph.

##### 889 Comparison of Full Graph Methods of Switched Circuits Solution

**Authors:**
Zdeňka Dostálová,
David Matoušek,
Bohumil Brtnik

**Abstract:**

**Keywords:**
Switched capacitors of two phases,
switched
currents of two phases,
transformation graph,
two-graph,
Mason's
formula,
voltage transfer,
summary graph.

##### 888 Speedup Breadth-First Search by Graph Ordering

**Abstract:**

Breadth-First Search (BFS) is a core graph algorithm that is widely used for graph analysis. As it is frequently used in many graph applications, improving the BFS performance is essential. In this paper, we present a graph ordering method that could reorder the graph nodes to achieve better data locality, thus, improving the BFS performance. Our method is based on an observation that the sibling relationships will dominate the cache access pattern during the BFS traversal. Therefore, we propose a frequency-based model to construct the graph order. First, we optimize the graph order according to the nodes’ visit frequency. Nodes with high visit frequency will be processed in priority. Second, we try to maximize the child nodes’ overlap layer by layer. As it is proved to be NP-hard, we propose a heuristic method that could greatly reduce the preprocessing overheads.We conduct extensive experiments on 16 real-world datasets. The result shows that our method could achieve comparable performance with the state-of-the-art methods while the graph ordering overheads are only about 1/15.

**Keywords:**
Breadth-first search,
BFS,
graph ordering,
graph algorithm.

##### 887 On Detour Spectra of Some Graphs

**Authors:**
S.K.Ayyaswamy,
S.Balachandran

**Abstract:**

**Keywords:**
Detour eigenvalue (of a graph),
detour spectrum(of a graph),
detour energy(of a graph),
detour - equienergetic graphs.

##### 886 Analysis of Electrical Networks Using Phasors: A Bond Graph Approach

**Authors:**
Israel Núñez-Hernández,
Peter C. Breedveld,
Paul B. T. Weustink,
Gilberto Gonzalez-A

**Abstract:**

This paper proposes a phasor representation of electrical networks by using bond graph methodology. A so-called phasor bond graph is built up by means of two-dimensional bonds, which represent the complex plane. Impedances or admittances are used instead of the standard bond graph elements. A procedure to obtain the steady-state values from a phasor bond graph model is presented. Besides the presentation of a phasor bond graph library in SIDOPS code, also an application example is discussed.

**Keywords:**
Bond graphs,
phasor theory,
steady-state,
complex
power,
electrical networks.

##### 885 Topological Queries on Graph-structured XML Data: Models and Implementations

**Authors:**
Hongzhi Wang,
Jianzhong Li,
Jizhou Luo

**Abstract:**

**Keywords:**
XML,
Graph Structure,
Topological query.

##### 884 An Efficient Graph Query Algorithm Based on Important Vertices and Decision Features

**Authors:**
Xiantong Li,
Jianzhong Li

**Abstract:**

**Keywords:**
Decision Feature,
Frequent Feature,
Graph Dataset,
Graph Query

##### 883 Notes on Fractional k-Covered Graphs

**Authors:**
Sizhong Zhou,
Yang Xu

**Abstract:**

**Keywords:**
graph,
binding number,
fractional k-factor,
fractional k-covered graph.

##### 882 Automatic Fingerprint Classification Using Graph Theory

**Authors:**
Mana Tarjoman,
Shaghayegh Zarei

**Abstract:**

Using efficient classification methods is necessary for automatic fingerprint recognition system. This paper introduces a new structural approach to fingerprint classification by using the directional image of fingerprints to increase the number of subclasses. In this method, the directional image of fingerprints is segmented into regions consisting of pixels with the same direction. Afterwards the relational graph to the segmented image is constructed and according to it, the super graph including prominent information of this graph is formed. Ultimately we apply a matching technique to compare obtained graph with the model graphs in order to classify fingerprints by using cost function. Increasing the number of subclasses with acceptable accuracy in classification and faster processing in fingerprints recognition, makes this system superior.

**Keywords:**
Classification,
Directional image,
Fingerprint,
Graph,
Super graph.

##### 881 Graphs with Metric Dimension Two-A Characterization

**Authors:**
Sudhakara G,
Hemanth Kumar A.R

**Abstract:**

In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. β (G) = 2 ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever β (G) = 2 . We also find a bound for cardinality of any distance partite set with reference to a given vertex, when ever β (G) = 2 . Also, in a graph G with β (G) = 2 , a bound for cardinality of any distance partite set as well as a bound for number of vertices in any sub graph H of G is obtained in terms of diam H .

**Keywords:**
Metric basis,
Distance partition,
Metric dimension.

##### 880 Image Segmentation Using Suprathreshold Stochastic Resonance

**Authors:**
Rajib Kumar Jha,
P.K.Biswas,
B.N.Chatterji

**Abstract:**

In this paper a new concept of partial complement of a graph G is introduced and using the same a new graph parameter, called completion number of a graph G, denoted by c(G) is defined. Some basic properties of graph parameter, completion number, are studied and upperbounds for completion number of classes of graphs are obtained , the paper includes the characterization also.

**Keywords:**
Completion Number,
Maximum Independent subset,
Partial complements,
Partial self complementary.

##### 879 Analysis of a Singular Perturbed Synchronous Generator with a Bond Graph Approach

**Authors:**
Gilberto Gonzalez-A,
Noe Barrera-G

**Abstract:**

**Keywords:**
Bond graph modelling,
synchronous generator,
singular perturbations

##### 878 Connected Vertex Cover in 2-Connected Planar Graph with Maximum Degree 4 is NP-complete

**Authors:**
Priyadarsini P. L. K,
Hemalatha T.

**Abstract:**

**Keywords:**
NP-complete,
2-Connected planar graph,
block,
cut vertex

##### 877 Evolutionary Dynamics on Small-World Networks

**Authors:**
Jan Rychtar,
Brian Stadler

**Abstract:**

**Keywords:**
evolutionary dynamics,
small-world networks

##### 876 Eccentric Connectivity Index, First and Second Zagreb Indices of Corona Graph

**Authors:**
A. Kulandai Therese

**Abstract:**

The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics. In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub divisionrelated corona graphs.

**Keywords:**
Corona graph,
Degree,
Eccentricity,
Eccentric
Connectivity Index,
First Zagreb index,
Second Zagreb index and
Subdivision graphs.

##### 875 Analysis of a Hydroelectric Plant connected to Electrical Power System in the Physical Domain

**Authors:**
Gilberto Gonzalez-A,
Octavio Barriga

**Abstract:**

**Keywords:**
Bond graph,
hydraulic plant,
steady state.

##### 874 Image Segmentation Based on Graph Theoretical Approach to Improve the Quality of Image Segmentation

**Authors:**
Deepthi Narayan,
Srikanta Murthy K.,
G. Hemantha Kumar

**Abstract:**

**Keywords:**
Graph based image segmentation,
threshold,
Weighted Euclidean distance.