Wiener polarity and Wiener index of double generalized Petersen graph

Abstract

A topological index is a numerical parameter of a graph which characterizes some of the topological properties of the graph. The concepts of Wiener polarity index and Wiener index were established in chemical graph theory by means of the distances. The double generalized Petersen graph denoted by DP(n,k) is obtained by attaching the vertices of outer pendent vertices to inner pendent vertices lying at distance k. The length of the outer and inner cycle is n, thus the number of vertices are 4n and the number of edges in the DP(n,k) are 6n. In this paper, the Wiener polarity index of DP(n,k for 3≤n≤6 and for n≥6k+1 is computed. Further, the Wiener index of DP(n,k), for k={1,2} is determined.

Keywords

• 05C22
• 05C12