Global Domination Integrity of Graphs
Sultan Senan Mahde, Veena Mathad · Mathematical Sciences Letters · 2017
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.