INTEGRITY AND DOMINATION INTEGRITY OF GEAR GRAPHS

Abstract

C.A. Barefoot, et. al. [4] introduced the concept of the integrity of agraph. It is an useful measure of vulnerability and it is defined as follows. I(G) =min{|S| + m(G - S) : S ? V (G)}, where m(G - S) denotes the order of the largestcomponent in G- S. Unlike the connectivity measures, integrity shows not only thedifficulty to break down the network but also the damage that has been caused. Asubset S of V (G) is said to be an I-set if I(G) =|S| + m(G - S). We introduced a newvulnerability parameter in [4],namely domination integrity of a graph G. It is a definedas DI(G) = min{|S| + m(G - S)}, where S is a dominating set of G and m(G - S)denotes the order of the largest component in G- S. K.S. Bagga,et. al. [2] gave aformula for I(K2× Cn). In this paper, we give a correct formula for I(K2× Cn). Wefind some results on the integrity and domination integrity of gear graphs.