Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 02 03 The $r$-dynamic chromatic number of the corona product of graphs 14896 10.22049/cco.2025.29285.1926 EN Sampathkumar R. Department of Mathematics, Annamalai University, Annamalainagar - 608 002, India S. Anantharaman Department of Mathematics, Annamalai University, Annamalainagar - 608 002, India Journal Article 2023 12 23 Let $G$ be a graph. An {\it $r\!$-dynamic $k\!$-coloring} of $G$ is a proper $k\!$-coloring of $G$ such that every vertex $v$ in $V(G)$ has neighbors in at least $\min\{r,d_G(v)\}$ different color classes. The {\it $r\!$-dynamic chromatic number} of $G,$ denoted by $\chi_r(G),$ is the least $k$ such that $G$ has an $r\!$-dynamic $k\!$-coloring. We determine the $r\!$-dynamic chromatic number of the corona product $G\odot H$ of graphs $G$ and $H,$ in terms of the dynamic chromatic numbers of $G$ and $H.$ https://comb-opt.azaruniv.ac.ir/article_14896_299bd2a815fd540bc711816391e64ab9.pdf