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Indian Journal of Pure and Applied Mathematics

, Volume 49, Issue 4, pp 591–600 | Cite as

r-Dynamic Chromatic Number of Some Line Graphs

  • Hanna FurmańczykEmail author
  • J. Vernold Vivin
  • N. Mohanapriya
Article
  • 76 Downloads

Abstract

An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that |c(N(v))| ≥ min {r, deg(v)}, for each vV (G). The r-dynamic chromatic number of a graph G is the smallest k such that G admits an r-dynamic coloring with k colors. In this paper, we obtain the r-dynamic chromatic number of the line graph of helm graphs Hn for all r between minimum and maximum degree of Hn. Moreover, our proofs are constructive, what means that we give also polynomial time algorithms for the appropriate coloring. Finally, as the first, we define an equivalent model for edge coloring.

Key words

r-dynamic coloring conditional coloring line graph helm graph 

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Copyright information

© The Indian National Science Academy 2018

Authors and Affiliations

  • Hanna Furmańczyk
    • 1
    Email author
  • J. Vernold Vivin
    • 2
  • N. Mohanapriya
    • 3
  1. 1.Faculty of Mathematics, Physics and Informatics, Institute of InformaticsUniversity of Gdańsk, Wita StwoszaGdańskPoland
  2. 2.Department of MathematicsUniversity College of Engineering Nagercoil, (Anna University Constituent College)Konam, NagercoilIndia
  3. 3.Department of MathematicsKongunadu Arts and Science CollegeCoimbatoreIndia

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