Abstract
R. Sundareswaran and V. Swaminathan [11], introduced the concept of the domination integrity of a graph. It is a useful measure of vulnerability and it is defined as DI(G) = min{|S|+m(G−S), where S is a dominating set and m(G−S) is the order of a maximum component of G−S}. In this paper we introduce the concept of global domination integrity of a graph G, and define it as GDI(G) = min{|S|+m(G−S), where S is a global dominating set and m(G−S) is the order of a maximum component of G−S}. The global domination integrity of some graphs is obtained. The relations between global domination integrity and other parameters are determined.
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