On vulnerability and domination concept in communication networks

In this thesis, the integrity parameter based on the concept of domination was discussed in communication networks, the previous studies on this subject were examined and the domination integrity values of some graph classes were found. A new vulnerability measure of domination integrity was introduced by Sundareswaran and Swaminathan 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. Domination integrity of wheel graph W_(1,n), ladder graph L_n, double star S_(m,n), bistar B_(n,n), friendship F_n, thorn graphs of P_n and C_n which are commonly used network models were investigated and the results were generalized.