THE AVERAGE LOWER REINFORCEMENT NUMBER OF A GRAPH

摘要

Let G = (V (G), E(G)) be a simple undirected graph. The reinforcement number of a graph is a vulnerability parameter of a graph. We have investigated a refinement that involves the average lower reinforcement number of this parameter. The lower reinforcement number, denoted by r(e*) (G), is the minimum cardinality of reinforcement set in G that contains the edge e* of the complement graph G. The average lower reinforcement number of G is defined by r(av)(G) = 1/ |E(G)| Sigma(e*)is an element of E((G) over bar) r(e*) (G).