RESIDUAL CLOSENESS FOR HELM AND SUNFLOWER GRAPHS

Abstract

Vulnerability is an important concept in network analysis related with theability of the network to avoid intentional attacks or disruption when a failure is producedin some of its components. Often enough, the network is modeled as an undirected andunweighted graph in which vertices represent the processing elements and edges representthe communication channel between them. Different measures for graph vulnerabilityhave been introduced so far to study different aspects of the graph behavior after removalof vertices or links such as connectivity, toughness, scattering number, binding numberand integrity. In this paper, we consider residual closeness which is a new characteristicfor graph vulnerability. Residual closeness is a more sensitive vulnerability measure thanthe other measures of vulnerability. We obtain exact values for closeness, vertex residualcloseness (VRC) and normalized vertex residual closeness (NVRC) for some wheel relatedgraphs namely helm and sunflower