Journal of Prime Research in Mathematics

# Exact wiener indices of the strong product of graphs

K. Pattabiraman
Department of Mathematics, Faculty of Engineering and Technology, Annamalai University, Annamalainagar, India.

$$^{1}$$Corresponding Author: pramank@gmail.com

### Abstract

The Wiener index, denoted by $$W(G)$$, of a connected graph $$G$$ is the sum of all pairwise distances of vertices of the graph, that is, $$W(G) = \frac{1}{2} \sum_{u,v∈V (G)}d(u, v)$$. In this paper, we obtain the Wiener index of the strong product of a path and a cycle and strong product of two cycles.

#### Keywords:

Strong product, Wiener index