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On r-dynamic coloring of comb graphs

2021
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Notes on Number Theory and Discrete Mathematics
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An r-dynamic coloring of a graph G is a proper coloring of G such that every vertex in V(G) has neighbors in at least $\min\{d(v),r\}$ different color classes. The r-dynamic chromatic number of graph G denoted as $\chi_r (G)$, is the least k such that G has a coloring. In this paper we obtain the r-dynamic chromatic number of the central graph, middle graph, total graph, line graph, para-line graph and sub-division graph of the comb graph $P_n\odot K_1$ denoted by $C(P_n\odot K_1), M(P_n\odot

doi:10.7546/nntdm.2021.27.2.191-200
fatcat:mw5i7a7jljdrfop6z26ltta5aa