<Emphasis Type="Italic">r</Emphasis>-Dynamic Chromatic Number of Some Line Graphs |
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| Authors: | Hanna Furmańczyk J Vernold Vivin N Mohanapriya |
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| Institution: | 1.Faculty of Mathematics, Physics and Informatics, Institute of Informatics,University of Gdańsk, Wita Stwosza,Gdańsk,Poland;2.Department of Mathematics,University College of Engineering Nagercoil, (Anna University Constituent College),Konam, Nagercoil,India;3.Department of Mathematics,Kongunadu Arts and Science College,Coimbatore,India |
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| 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. |
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