Geodesic
Optimal adjacent vertex-distinguishing edge-colorings of circulant graphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1341-1359

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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 χ_a^' (G). We prove that χ_a^'(G)=2R+1 for most circulant graphs C_n( [[ 1,R ]] ).
Keywords: proper edge-coloring, circulant graph, distinguishing vertices, adjacent vertex-distinguishing, chromatic number 
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Gravier, Sylvain; Signargout, Hippolyte; Slimani, Souad. Optimal adjacent vertex-distinguishing edge-colorings of circulant graphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1341-1359. http://geodesic.mathdoc.fr/item/DMGT_2024_44_4_a6/