A Study on the Differential Value of Total Graph

Abstract

Let be a graph and X be a subset of V. Let be the set of vertices in V − X that has a neighbour in a set X. The differential of a set X, is defined as ∂(X) which is |B(X)| − |X| and the differential of a graph is ∂(G) = max {∂(X)/X ⊂ V}. The total graph T (G) of a graph G is the graph whose vertex set is V (G) ∪ E(G) with two vertices of T (G) being adjacent if and only if the corresponding elements of G are either adjacent or incident. In this paper, we study the differential value of total graph for some standard graphs and its bounds.