Geodesic
Vertex distinguishing proper edge colorings of the corona products of graphs
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 2, pp. 47-56.

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A proper edge coloring of a graph $G$ is a mapping $f:E(G)\longrightarrow\mathbb{Z}_{\geq 0}$ such that $f(e)\not=f(e')$ for every pair of adjacent edges $e$ and $e'$ in $G$. A proper edge coloring $f$ of a graph $G$ is called vertex distinguishing, if for any different vertices $u,v \in V(G)$, $S(u, f) \ne S(v, f)$, where $S(v, f) = \{f(e) \ | \ e = uv \in E(G)\}$. The minimum number of colors required for a vertex distinguishing proper coloring of a graph $G$ is denoted by $\chi'_{vd}(G)$ and called vertex distinguishing chromatic index of $G$. In this paper we provide lower and upper bounds on the vertex distinguishing chromatic index of the corona products of graphs.
Keywords: edge coloring, proper edge coloring, vertex distinguishing proper coloring, corona product 
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T. K. Petrosyan. Vertex distinguishing proper edge colorings of the corona products of graphs. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 2, pp. 47-56. http://geodesic.mathdoc.fr/item/UZERU_2024_58_2_a1/

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