On Powers of Some Graph Operations

Abstract

Let G*H be the product * of G and H. In this paper we determine the rth power of the graph G*H in terms of Gr, Hrand Gr*Hr, when * is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation (G*H)r=Gr*Hr. We also compute the Wiener index and Wiener polarity index of the skew product.

Keywords

• graph product
• power graphs
• graph indices