Edge-Neighbor Rupture Degree on Graph Operations

Abstract

Vulnerability and reliability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links in a communication network. An edge subversion strategy of a graph , say , is a set of edge(s) in whose adjacent vertices which is incident with the removal edge(s) are removed from . The survival subgraph is denoted by − . The edgeneighbor-rupture degree of connected graph , , is defined to be = − − | | − − : ⊆ , − ≥ 1 where is any edge-cut-strategy of , − is the number of the components of − , and − is the maximum order of the components of − . In this paper we give some results for the edge-neighbor-rupture degree of the graph operations and Thorny graph types are examined.