¹School of Information and Technology, Yunnan Normal University, Kunming 650500, China
²Editorial Department of Yunnan Normal University, Kunming 650092, China
³Key Laboratory of Educational Informatization for Nationalities, Ministry of Education, Yunnan Normal University, Kunming 650500, China

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Abstract—The isolated toughness and binding number, as the parameters for measuring stability and vulnerable of networks, have been widely used in computer communication networks. The concept of fractional critical deleted graph is used to measure whether there exists a feasible data packet transmission scheme from site to site when certain intermediate channels and sites are damaged. In this paper, we study the relationship between fractional critical deleted graph and vulnerability parameters. It is highlighted that a graph G is a fractional critical deleted graph if its isolated toughness or binding number meets certain conditions. Furthermore, some conditions we give in the article is sharp in some sense.

Index Terms—vulnerable of networks, isolated toughness, binding number, fractional (g; f)-factor, fractional (g; f; n′)- critical deleted graph, fractional (g; f; n′;m)-critical deleted graph

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Cite: Wei Gao, Yun Gao, Tianwei Xu, Li Liang, "Vulnerability of Networks and Existence of Fractional Factor Avoiding Certain Channels and Sites," Journal of Computers vol. 9, no. 7, pp. 1712-1722, 2014.