Note on Strong Product of Graphs

M. Tavakoli, F. Rahbarnia, A. R. Ashrafi

Let $G$ and $H$ be graphs. The strong product $ G\boxtimes H$ of graphs $G$ and $H$ is the graph with vertex set $V(G)\times V(H)$ and $u = (u_1, v_1)$ is adjacent with $v = (u_2, v_2)$ whenever ($v_1 = v_2$ and $u_1$ is adjacent with $u_2$) or ($u_1 = u_2$ and $v_1$ is adjacent with $v_2$) or ($u_1$ is adjacent with $u_2$ and $v_1$ is adjacent with $v_2$). In this paper, we study some properties of this operation. Also, we obtain lower and upper bounds for Wiener and hyper-Wiener indices of Strong product of graphs.