r-Dynamic Chromatic Number of Some Line Graphs

Hanna Furmańczyk (), J. Vernold Vivin () and N. Mohanapriya ()
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Hanna Furmańczyk: University of Gdańsk, Wita Stwosza
J. Vernold Vivin: University College of Engineering Nagercoil, (Anna University Constituent College)
N. Mohanapriya: Kongunadu Arts and Science College

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 4, 591-600

Abstract: 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 v ∈ V (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.

Keywords: r-dynamic coloring; conditional coloring; line graph; helm graph (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0288-1

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