Geodesic
Note on Strong Product of Graphs
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 1, p. 187

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
Classification : 05C76 05C12 05C07
Keywords: Strong product, Wiener index, Eulerian graph. 
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     author = {M. Tavakoli and F. Rahbarnia and A. R. Ashrafi},
     title = {Note on {Strong} {Product} of {Graphs}},
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M. Tavakoli; F. Rahbarnia; A. R. Ashrafi. Note on Strong Product of Graphs. Kragujevac Journal of Mathematics, Tome 37 (2013) no. 1, p. 187 . http://geodesic.mathdoc.fr/item/KJM_2013_37_1_a13/