Abstract
The 2-distance vertex-distinguishing index \(\chi '_\mathrm{d2}(G)\) of a graph G is the minimum number of colors required for a proper edge coloring of G such that any pair of vertices at distance two have distinct sets of colors. It was conjectured that every subcubic graph G has \(\chi '_{\mathrm{d2}}(G)\le 5\). In this paper, we confirm this conjecture for subcubic graphs with maximum average degree less than \(\frac{8}{3}\).
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Communicated by Sandi Klavžar.
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Research supported by NSFC (No. 11771402).
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Victor, L.K., Liu, J. & Wang, W. Two-Distance Vertex-Distinguishing Index of Sparse Subcubic Graphs. Bull. Malays. Math. Sci. Soc. 43, 3183–3199 (2020). https://doi.org/10.1007/s40840-019-00862-1
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DOI: https://doi.org/10.1007/s40840-019-00862-1
Keywords
- Subcubic graph
- Maximum average degree
- Edge coloring
- 2-Distance vertex-distinguishing index
- AVD edge coloring