On r-dynamic coloring of comb graphs

K. Kalaiselvi, Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, N. Mohanapriya, J. Vernold Vivin, PG and Department of Mathematics, Kongunadu Arts and Science College, Department of Mathematics, University College of Engineering Nagercoil
2021 Notes on Number Theory and Discrete Mathematics  
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 $C(P_n\odot K_1), M(P_n\odot
more » ... 1), T(P_n\odot K_1), L(P_n\odot K_1), P(P_n\odot K_1)$ and $S(P_n\odot K_1)$ respectively by finding the upper bound and lower bound for the r-dynamic chromatic number of the Comb graph.
doi:10.7546/nntdm.2021.27.2.191-200 fatcat:mw5i7a7jljdrfop6z26ltta5aa