Geodesic
Note on Strong Product of Graphs
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 1, p. 187 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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. 
@article{KJM_2013_37_1_a13,
     author = {M. Tavakoli and F. Rahbarnia and A. R. Ashrafi},
     title = {Note on {Strong} {Product} of {Graphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {187 },
     year = {2013},
     volume = {37},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2013_37_1_a13/}
}
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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/