Edge-Neighbor-Rupture Degree of Graphs

Abstract EN

The edge-neighbor-rupture degree of a connected graph G is defined to be ENRG=maxωG−S−S−mG−S:S⊆EG,ωG−S≥1, where S is any edge-cut-strategy of G, ωG−S is the number of the components of G−S, and mG−S is the maximum order of the components of G−S.

In this paper, the edge-neighbor-rupture degree of some graphs is obtained and the relations between edge-neighbor-rupture degree and other parameters are determined.