**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**430

# Search results for: fractional k-covered graph.

##### 430 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.

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

**Authors:**
Sizhong Zhou,
Yang Xu

**Abstract:**

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

##### 428 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.

##### 427 Fractional Masks Based On Generalized Fractional Differential Operator for Image Denoising

**Authors:**
Hamid A. Jalab,
Rabha W. Ibrahim

**Abstract:**

This paper introduces an image denoising algorithm based on generalized Srivastava-Owa fractional differential operator for removing Gaussian noise in digital images. The structures of nxn fractional masks are constructed by this algorithm. Experiments show that, the capability of the denoising algorithm by fractional differential-based approach appears efficient to smooth the Gaussian noisy images for different noisy levels. The denoising performance is measured by using peak signal to noise ratio (PSNR) for the denoising images. The results showed an improved performance (higher PSNR values) when compared with standard Gaussian smoothing filter.

**Keywords:**
Fractional calculus,
fractional differential operator,
fractional mask,
fractional filter.

##### 426 Fractional Order Feedback Control of a Ball and Beam System

**Authors:**
Santosh Kr. Choudhary

**Abstract:**

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

**Keywords:**
Fractional order calculus,
fractional order controller,
fractional order system,
ball and beam system,
PIλDμ controller,
modelling,
simulation.

##### 425 Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing

**Authors:**
Changhong Guo,
Shaomei Fang,
Yong He

**Abstract:**

**Keywords:**
European option pricing,
fractional Black-Scholes
equations,
fractional G-Brownian motion,
Taylor’s series of fractional
order,
uncertain volatility.

##### 424 Existence of Iterative Cauchy Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

**Keywords:**
Fractional calculus,
fractional differential equation,
Cauchy equation,
Riemann-Liouville fractional operators,
Volterra
integral equation,
non-expansive mapping,
iterative differential equation.

##### 423 Stability of Interval Fractional-order Systems with Order 0 < α < 1

**Authors:**
Hong Li,
Shou-ming Zhong,
Hou-biao Li

**Abstract:**

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

**Keywords:**
Interval fractional-order systems,
linear matrix inequality (LMI),
asymptotical stability.

##### 422 Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems

**Authors:**
Ali Dorostkar

**Abstract:**

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

**Keywords:**
Tangent line,
fractional dimension,
root,
optimization problem.

##### 421 Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems

**Authors:**
Kazem Ghanbari,
Yousef Gholami

**Abstract:**

**Keywords:**
Fractional derivatives and integrals,
Hamiltonian
system,
Lyapunov type inequalities,
stability,
disconjugacy.

##### 420 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.

##### 419 Application of Fractional Model Predictive Control to Thermal System

**Authors:**
Aymen Rhouma,
Khaled Hcheichi,
Sami Hafsi

**Abstract:**

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller*.*

**Keywords:**
Fractional model predictive control,
fractional order systems,
thermal system.

##### 418 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.

##### 417 Realization of Fractional-Order Capacitors with Field-Effect Transistors

**Authors:**
Steve Hung-Lung Tu,
Yu-Hsuan Cheng

**Abstract:**

**Keywords:**
Fractional-order,
field-effect transistors,
RC
transmission lines.

##### 416 Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI

**Authors:**
Elham Amini Boroujeni,
Hamid Reza Momeni

**Abstract:**

**Keywords:**
Fractional order calculus,
Fractional order observer,
Linear matrix inequality,
Nonlinear Systems,
Observer based
Controller.

##### 415 A Design of Fractional-Order PI Controller with Error Compensation

**Authors:**
Mazidah Tajjudin,
Norhashim Mohd Arshad,
Ramli Adnan

**Abstract:**

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

**Keywords:**
Fractional-order PI,
Ziegler-Nichols tuning,
Oustaloup's Recursive Approximation,
steam temperature control.

##### 414 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.

##### 413 Some Remarks About Riemann-Liouville and Caputo Impulsive Fractional Calculus

**Authors:**
M. De la Sen

**Abstract:**

**Keywords:**
Rimann- Liouville fractional calculus,
Caputofractional derivative,
Dirac delta,
Distributional derivatives,
Highorderdistributional derivatives.

##### 412 Oil Displacement by Water in Hauterivian Sandstone Reservoir of Kashkari Oil Field

**Authors:**
A. J. Nazari,
S. Honma

**Abstract:**

This paper evaluates oil displacement by water in Hauterivian sandstone reservoir of Kashkari oil field in North of Afghanistan. The core samples of this oil field were taken out from well No-21^{st}, and the relative permeability and fractional flow are analyzed. Steady state flow laboratory experiments are performed to empirically obtain the fractional flow curves and relative permeability in different water saturation ratio. The relative permeability represents the simultaneous flow behavior in the reservoir. The fractional flow approach describes the individual phases as fractional of the total flow. The fractional flow curve interprets oil displacement by water, and from the tangent of fractional flow curve can find out the average saturation behind the water front flow saturation. Therefore, relative permeability and fractional flow curves are suitable for describing the displacement of oil by water in a petroleum reservoir. The effects of irreducible water saturation, residual oil saturation on the displaceable amount of oil are investigated through Buckley-Leveret analysis.

**Keywords:**
Fractional flow,
oil displacement,
relative permeability,
simultaneously flow.

##### 411 An Efficient Hamiltonian for Discrete Fractional Fourier Transform

**Authors:**
Sukrit Shankar,
Pardha Saradhi K.,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Hamiltonian,
Eigen
Vectors,
Discrete Hermite Gaussians.

##### 410 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.

##### 409 Lower Bound of Time Span Product for a General Class of Signals in Fractional Fourier Domain

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

**Keywords:**
Fractional Fourier Transform,
uncertainty principle,
Fractional Fourier Span,
amplitude,
phase.

##### 408 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.

##### 407 Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Perturbation,
Fractional Fourier span,
amplitude,
phase,
transform order,
filterbanks.

##### 406 Quality Factor Variation with Transform Order in Fractional Fourier Domain

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
K. Pardha Saradhi,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Quality Factor,
Fractional Fourier span,
transient signals.

##### 405 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

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

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

**Abstract:**

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

##### 403 Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals

**Authors:**
Manoj Singh,
Mumtaz Ahmad Khan,
Abdul Hakim Khan

**Abstract:**

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral.

**Keywords:**
Fractional Derivatives and Integrals,
Hypergeometric
functions.

##### 402 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.

##### 401 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.