Residual Closeness in Cycles and Related Networks

Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. The main aim is to understand, predict, and possibly even control the behavior of a networked system under attacks or disfunctions of any type. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far. In this paper, we study the vulnerability of cycles and related graphs to the failure of individual vertices, using a measure called residual closeness which provides a more sensitive characterization of the graph than some other well-known vulnerability measures.

[1]  D. West.  Introduction to Graph Theory , 1995 .

[2]  Jian-Hua Yin,et al.  On the fault-tolerant diameter and wide diameter of omega-connected graphs , 2005, Networks.

[3]  Jian-Hua Yin,et al.  On the fault-tolerant diameter and wide diameter of ω-connected graphs , 2005 .

[4]  C. Dangalchev.  Residual closeness in networks , 2006 .

[5]  Chavdar Dangalchev,et al.  Residual Closeness and Generalized Closeness , 2011, Int. J. Found. Comput. Sci..

[6]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[8]  Haruo Hosoya,et al.  On some counting polynomials in chemistry , 1988, Discret. Appl. Math..

[9]  M. Krishnamoorthy,et al.  Fault diameter of interconnection networks , 1987 .

[10]  Vasek Chvátal,et al.  Tough graphs and hamiltonian circuits , 1973, Discret. Math..

[11]  Uppaluri S. R. Murty,et al.  Graph Theory with Applications , 1978 .

[12]  M. Diudea.  HOSOYA POLYNOMIAL IN TORI , 2002 .

[13]  Cun-Hui Zhang,et al.  Measures of Network Vulnerability , 2007, IEEE Signal Processing Letters.

[14]  Jean-Claude Bermond,et al.  Surveys in Combinatorics: GRAPHS AND INTERCONNECTION NETWORKS: DIAMETER AND VULNERABILITY , 1983 .

[15]  A. Brandstädt,et al.  Graph Classes: A Survey , 1987 .

[16]  Mehdi Behzad,et al.  Graphs and Digraphs , 1981, The Mathematical Gazette.

[17]  D. R. Woodall.  The binding number of a graph and its Anderson number , 1973 .

[18]  Joseph A. Gallian,et al.  A Dynamic Survey of Graph Labeling , 2009, The Electronic Journal of Combinatorics.

[19]  I. Frisch,et al.  Analysis and Design of Survivable Networks , 1970 .

[20]  Aysun Ozan Aytaç,et al.  Residual Closeness of wheels and Related Networks , 2011, Int. J. Found. Comput. Sci..

[21]  Yeong-Nan Yeh,et al.  The Wiener polynomial of a graph , 1996 .

[22]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[23]  H. A. Jung,et al.  On a class of posets and the corresponding comparability graphs , 1978, J. Comb. Theory B.

[24]  Dragan Stevanovic,et al.  Hosoya polynomial of composite graphs , 2001, Discret. Math..