Abstract:
A strong edge-coloring of a graph $G$ is a mapping $\phi : E(G) \rightarrow \mathbb{N}$ such that the edges at distance $0$ or $1$ receive distinct colors. The minimum number of colors required for such a coloring is called the strong chromatic index of $G$ and is denoted by $\chi_s'(G)$. In this paper, we investigate the strong chromatic index of the Mycielskian $\mu(G)$ of graphs $G$ and corona products $G \odot H$ of graphs $G$ and $H$. In particular, we give tight lower and upper bounds on $\chi_s'(G \odot H)$. Moreover, we provide specific structural criteria, under which the upper bound is sharp. We also derive tight lower and upper bounds on $\chi_s'(\mu(G))$ for Mycielskian of graphs.
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