DOMINATION INTEGRITY OF SOME GRAPH CLASSES

摘要

The stability of a communication network has a great importance in network design. There are several vulnerability measures used to determine the resistance of network to the disruption in this sense. Domination theory provides a model to measure the vulnerability of a graph network. A new vulnerability measure of domination integrity was introduced by Sundareswaran in his Ph.D. thesis (Parameters of vulnerability in graphs (2010)) and defined as DI(G) = min{|S| + m(G - S):S is an element of V(G)} where m(G - S) denotes the order of a largest component of graph G - S and S is a dominating set of G. The domination integrity of an undirected connected graph is such a measure that works on the whole graph and also the remaining components of graph after any break down. Here we determine the domination integrity of wheel graph W-1,W-n, Ladder graph L-n, S-m,S-n, Friendship graph F-n, Thorn graph of P-n and C-n which are commonly used graph models in network design.