Domination integrity of some graph classes

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 ∈ 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 W1,n, Ladder graph Ln, Sm,n, Friendship graph Fn, Thorn graph of Pn and Cn which are commonly used graph models in network design.