r-Strong edge colorings of graphs |
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Authors: | S Akbari H Bidkhori |
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Institution: | a Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran b Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran |
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Abstract: | Let G be a graph and for any natural number r, denotes the minimum number of colors required for a proper edge coloring of G in which no two vertices with distance at most r are incident to edges colored with the same set of colors. In Z. Zhang, L. Liu, J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett. 15 (2002) 623-626] it has been proved that for any tree T with at least three vertices, . Here we generalize this result and show that . Moreover, we show that if for any two vertices u and v with maximum degree d(u,v)?3, then . Also for any tree T with Δ(T)?3 we prove that . Finally, it is shown that for any graph G with no isolated edges, . |
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Keywords: | 05C05 05C15 |
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