Vertex distinguishing proper edge colorings of the corona products of graphs

T. K. Petrosyan

Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 2, pp. 47-56

Résumé

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.

Détail

Keywords: edge coloring, proper edge coloring, vertex distinguishing proper coloring, corona product