2-Distance vertex-distinguishing index of subcubic graphs

Victor Loumngam Kamga, Weifan Wang (), Ying Wang and Min Chen
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Victor Loumngam Kamga: Zhejiang Normal University
Weifan Wang: Zhejiang Normal University
Ying Wang: Zhejiang Normal University
Min Chen: Zhejiang Normal University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 1, No 10, 108-120

Abstract: 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 $$\chi ^{\prime }_{\mathrm{d2}}(G)$$ χ d 2 ′ ( 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 $$\chi ^{\prime }_{\mathrm{d2}}(G)\le 6$$ χ d 2 ′ ( G ) ≤ 6 . Since the Peterson graph P satisfies $$\chi ^{\prime }_{\mathrm{d2}}(P)=5$$ χ d 2 ′ ( P ) = 5 , our solution is within one color from optimal.

Keywords: Subcubic graph; Edge coloring; 2-Distance vertex-distinguishing index; Star-chromatic index (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-018-0288-4

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