Neighbor Isolated Tenacity of Graphs

The tenacity of a graph is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbor isolated version of this parameter. The neighbor isolated tenacity of a noncomplete connected graph G is defined to be NIT(G) = min {|X |+ c(G/X) / i(G/X) , i(G/X) ≥ 1} where the minimum is taken over all X , the cut strategy of G , i (G /X )is the number of components which are isolated vertices of G /X and c (G /X ) is the maximum order of the components of G /X . Next, the relations between neighbor isolated tenacity and other parameters are determined and the neighbor isolated tenacity of some special graphs are obtained. Moreover, some results about the neighbor isolated tenacity of graphs obtained by graph operations are given.