ScienceAsia - Journal of The Science Society of Thailand

ABSTRACT: The scattering number is a measure of the vulnerability of a graph. In this paper we investigate a refinement that involves the neighbour isolated version of the parameter. The neighbour isolated scattering number of a noncomplete graph G is defined to be NIS(G)=max{i(G/X)−|X|:i(G/X)≥1} where the maximum is taken over all X, the cut strategy of G, and i(G/X) is the number of components which are isolated vertices of G/X. Like the scattering number itself, this is a measure of the vulnerability of a graph, but it is more sensitive. The relations between neighbour isolated scattering number and other parameters are determined and the neighbour isolated scattering number of trees and other families are obtained. We also give some results for the neighbour isolated scattering number of the graphs obtained by some graph operations.

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Neighbour isolated scattering number of graphs

Ersin Aslan