Edge-Neighbor Rupture Degree on Graph Operations

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.