On r-dynamic coloring of comb graphs

K. Kalaiselvi, N. Mohanapriya and J. Vernold Vivin
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 191—200
DOI: 10.7546/nntdm.2021.27.2.191-200
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Authors and affiliations

K. Kalaiselvi
Department of Mathematics, Dr. Mahalingam College of Engineering and Technology
Pollachi-642 003, Tamil Nadu, India

N. Mohanapriya
PG and Department of Mathematics, Kongunadu Arts and Science College
Coimbatore-641 029, Tamil Nadu, India

J. Vernold Vivin
Department of Mathematics, University College of Engineering Nagercoil
(A Constituent College of Anna University, Chennai)
Konam, Nagercoil-629 004, Tamil Nadu, India

Abstract

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 K_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.

Keywords

  • r-dynamic coloring
  • Comb graph
  • Central graph
  • Middle graph
  • Total graph
  • Line graph
  • Sub-division graph
  • Para-line graph

2020 Mathematics Subject Classification

  • 05C15
  • 05C75

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Cite this paper

Kalaiselvi, K., Mohanapriya, N., & Vernold Vivin, J. (2021). On r-dynamic coloring of comb graphs. Notes on Number Theory and Discrete Mathematics, 27(2), 191-200, doi: 10.7546/nntdm.2021.27.2.191-200.

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