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arXiv · 2004.12822

Optimal Adjacent Vertex-Distinguishing Edge-Colorings of Circulant Graphs

Sylvain Gravier·Hippolyte Signargout·Souad Slimani
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Abstract

A $k$-proper edge-coloring of a graph G is called adjacent vertex-distinguishing if any two adjacent vertices are distinguished by the set of colors appearing in the edges incident to each vertex. The smallest value $k$ for which $G$ admits such coloring is denoted by $\chi'_a(G)$. We prove that $\chi'_a(G) = 2R + 1$ for most circulant graphs $C_n([1, R])$.

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Sylvain Gravier, Hippolyte Signargout, Souad Slimani. 2020-04-27. Optimal Adjacent Vertex-Distinguishing Edge-Colorings of Circulant Graphs. https://arxiv.org/abs/2004.12822

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