Topological indices are used to correlate and predict several physical and chemical properties of chemical compounds especially carbon containing compounds. Determination of the expressions for topological indices of different derived graphs of a graph is a new and interesting problem in graph theory. In this paper, these expressions are established first time for a distance based index, namely Gutman index. In these expressions, the Gutman index of the derived graphs of a graph G is given in terms of some parameters of parent graph G.

Wiener index, DD index, Gutman index, degree of a vertex, distance between two vertices.