The $r$-dynamic edge coloring of a closed helm graph

Abstract

As a natural generalization of the classical coloring problem in graph theory, the dynamic coloring problem deals with the existence of a proper coloring c of a graph so that |c(N (v))| ≥ min{r, d(v)} for every vertex v. In this paper, we obtain the r-dynamic edge chromatic number of any given closed helm graph for any positive integer r. This coincides with the r-dynamic chromatic number of the line graph of a closed helm graph. 2020 Mathematics Subject Classification. 05C15.