Turaci T.Aslan E.2024-07-222024-07-22201628047346http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/15974Let 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 re∗(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 rav (G)=1/E(G) ∑e∗∈E(G) re∗(G). In this paper, we define the average lower reinforcement number of a graph and we present the exact values for some well-known graph families. © EDP Sciences 2016.EnglishAll Open Access; Green Open AccessNetwork securityAverage lower reinforcement numberConnectivityDomination numberGraph vulnerabilityNetwork designReinforcementArticle10.1051/ita/2016015