Maximum Connectivity And Some Vulnerability Parameters Of Double Graphs

A communication network can be modeled by a connected graph whose vertices repre-sent the stations and whose edges represent the lines of communication. The stability(orvulnerability) of a network is of prime importance to network designers. The stability ofa network is always determined by vulnerability parameters of corresponding graph. Thefirst such parameters one generally encounters are connectivity and edge-connectivity, butthey do not take into account what remains after destruction. Hence it is important todetermine the parameters such as, the scattering number, the toughness and the integrityof a graph. For a general graph, computing most of these vulnerability parameters areNP-hard.The double graph is defined as D[G] = G×T₂, where×stands for direct productof graphs and T2 is a total graph with 2 vertices, which is obtained from the completegraph K2 by adding a loop to every vertex. In this paper, we study maximum vertex-connectivity, maximum edge-connectivity and some vulnerability parameters of doublegraphs.