Abstract
Let G = (V (G), E(G)) be a simple, undirected graph. The vulnerability of a graph is a determination that includes certain properties of the graph not to be damaged after the removal of a number of vertices or edges. In this paper, the concept of independent average connectivity number is introduced as a new vulnerability measure and some bounds and independent average connectivity number of some well-known graph families are examined. Independent average connectivity will give the number of vertices that need to be removed to separate the pairs of vertices selected from the independent set in a graph G(V, E). Independent average connectivity number of a graph G(V, E) is denoted by kβ(G) and defined as kβ(G) = T I(G) ( n 2 ) where T I(G) is a total independence number of G(V, E) graph with n vertices. In this study, all the graphs considered simple, finite, and undirected.
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