INTEGRITY AND DOMINATION INTEGRITY OF GEAR GRAPHS

Abstract

C.A. Barefoot, et. al. [4] introduced the concept of the integrity of a graph. 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 largest component in G − S. Unlike the connectivity measures, integrity shows not only the difficulty to break down the network but also the damage that has been caused. A subset S of V G is said to be an I-set if I G = |S| + m G − S . We introduced a new vulnerability parameter in [4],namely domination integrity of a graph G. It is a defined as 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 a formula for I K2 × Cn . In this paper, we give a correct formula for I K2 × Cn . We find some results on the integrity and domination integrity of gear graphs