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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.
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Czasopismo
Rocznik
Tom
Strony
297--307
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Faculty of Engineering and Computer Sciences, Izmir University of Economics, 35330, Izmir, Turkey
autor
- Department of Mathematics, Faculty of Science, Ege University, 35100, Izmir, Turkey
Bibliografia
- [1] Aytac, A., Odabas, Z. N.: Residual Closeness of Wheels and Related Networks, International Journal of Foundations of Computer Science, 22(5), 2011, 1229-1240.
- [2] Banic, I., Erves, R., Zerovnik, J.: Edge, vertex and mixed fault diameters, Advances in Applied Mathematics, 43, 2009, 231-238.
- [3] Barefoot, C. A., Entringer, R., Swart, H.: Vulnerability in graphs—a comparative survey, Journal of Combinatorial Mathematics and Combinatorial Computing, 1, 1987, 13-22.
- [4] Bermond, J. C., Bond, J., Paoli, M., Peyrat, C.: Graphs and interconnection networks: diameter and vulnerability, London Mathematical Society Lecture Note Series, 82, 1983, 1-29.
- [5] Bondy, J. A., Murty, U. S. R.: Graph theory with applications, American Elsevier Publishing Co., Inc., New York, 1976.
- [6] Brandstadt, A., Le, V. B., Spinrad, J. P.: Graph classes: a survey, SIAM, Philadelphia, PA, 1999.
- [7] Chartrand G., Lesniak, L.: Graphs and Digraphs, Second Edition, Wadsworth, Monterey, 1986.
- [8] Chvatal, V.: Tough graphs and Hamiltonian circuits, Discrete Mathematics, 5, 1973, 215-228.
- [9] Dangalchev, Ch.: Residual closeness and generalized closeness, International Journal of Foundations of Computer Science, 22(8), 2011, 1939-1948.
- [10] Dangalchev, Ch.: Residual Closeness in Networks, Physica A, 365(2), 2006, 556-564.
- [11] Diudea, M. V.: Hosoya polynomial in tori, MATCH Communications in Mathematical and in Computer Chemistry, 45, 2002, 109-122.
- [12] Frank, H., Frisch, I. T.: Analysis and design of survivable networks, IEEE Transactions on Communications Technology, 18(5), 1970, 501-519.
- [13] Gallian, J. A.: A dynamic survey of graph labeling, Electronic Journal of Combinatorics, 15, 2008, DS6.
- [14] Gutman, I., KlavZar, S., Petkovsek, M., Zigert, P.: On Hosoya polynomials of benzenoid graphs, MATCH Communications in Mathematical and in Computer Chemistry, 43, 2001,49-66.
- [15] Hosoya, H.: On some counting polynomials in chemistry, Discrete Applied Mathematics, 19, 1988, 239-257.
- [16] Jung, H. A.: On a class of posets and the corresponding comparability graphs, Journal of Combinatorial Theory, Series B, 24(2), 1978, 125-133.
- [17] Krishnamoorthy, M., Krishnamurty, B.: Fault diameter of interconnection networks, Computers & Mathematics with Applications, 13, 1987, 577-582.
- [18] Sagan, B. E., Yeh, Y. -N., Zhang, P.: The Wiener Polynomial of a Graph, International Journal of Quantum Chemistry, 60(5), 1996, 959-969.
- [19] Stevanovic, D.: Hosoya polynomial of composite graphs, Discrete Mathematics, 235, 2001, 237-244.
- [20] Vaidya, S. K., Kanani, K.K.: Some Cycle Related Product Cordial Graphs, International Journal of Algorithms, Computing and Mathematics, 3(1), 2010, 1-8.
- [21] Vardi, Y., Zhang, C. H.: Measures of Network Vulnerability, IEEE Signal Processing Letters, 14(5), 2007, 313-316.
- [22] West, D. B.: Introduction to Graph Theory, Prentice Hall, NJ, 2001.
- [23] Woodall, D. R.: The binding number of a graph and its Anderson number, Journal of Combinatorial Theory, Series B, 15, 1973, 225-255.
- [24] Yin, J. H., Li, J. S., Chen, G. L., Zhong, C.: On the fault-tolerant diameter and wide diameter of omega- connected graphs, Networks, 45, 2005, 88-94.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a050d937-2d00-484c-95f7-7745e71292e2