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2-Distance vertex-distinguishing index of subcubic graphs

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Abstract

A 2-distance vertex-distinguishing edge coloring of a graph G is a proper edge coloring of G such that any pair of vertices at distance 2 have distinct sets of colors. The 2-distance vertex-distinguishing index \(\chi ^{\prime }_{\mathrm{d2}}(G)\) of G is the minimum number of colors needed for a 2-distance vertex-distinguishing edge coloring of G. Some network problems can be converted to the 2-distance vertex-distinguishing edge coloring of graphs. It is proved in this paper that if G is a subcubic graph, then \(\chi ^{\prime }_{\mathrm{d2}}(G)\le 6\). Since the Peterson graph P satisfies \(\chi ^{\prime }_{\mathrm{d2}}(P)=5\), our solution is within one color from optimal.

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Correspondence to Weifan Wang.

Additional information

Weifan Wang: Research supported by NSFC (No. 11771402);

Min Chen: Research supported by NSFC (Nos. 11471293, 11671053).

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Loumngam Kamga, V., Wang, W., Wang, Y. et al. 2-Distance vertex-distinguishing index of subcubic graphs. J Comb Optim 36, 108–120 (2018). https://doi.org/10.1007/s10878-018-0288-4

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  • DOI: https://doi.org/10.1007/s10878-018-0288-4

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