Average lower independence number in splitting graphs

Let G be a graph. The splitting graph S(G) for a graph G is obtained by adding a new vertex v' corresponding to each vertex v of G such that N(v) = N(v), where N(v) and N(v) are neighborhood sets of v and v, respectively. The average lower independence number i-(subscript(av))( G) of a graph G is defined as 1/|v|sum(iv(G) , where iv)(G) is the minimum cardinality of a maximal independent set that contains v . In this paper, we consider the average lower independence number in splitting graph. We determine the average lower independence number of S(G) for specific graphs G .