A Survey on Tenacity ParameterPart I

Abstract

If we think of the graph as modeling a network, the vulnerability measurethe resistance of the network to disruption of operation after the failure of certainstations or communication links. In assessing the "vulnerability"of a graph one determines the extent to which the graph retains certainproperties after the removal of vertices and / or edges. Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number, tenacity and... . In this paper we survey and discuss tenacity and its properties in vulnerability calculation and we will comparedifferent measures of vulnerability with tenacity for several classes ofgraphs.