Differential value of splitting and middle graph of some standard graphs

Abstract

Let G = (V,E) be a graph and X be a subset of V. Let B(X) be the set of vertices in V−X that has a neighbour in a set X. The differential of set X is defined as ∂(X) is |B(X)|−|X| and the differential of a graph is defined as ∂(G) = max{∂(X)/X⊂V}. In this paper, we obtain the differential value of middle and splitting graph for path, cycle, star, wheel and complete graph.