IJPAM: Volume 106, No. 8 (2016)

ON DYNAMIC COLORING OF FAN GRAPHS

N. Mohanapriya$^1$, Vivin J. Vernold$^2$, M. Venkatachalam$^3$
$^{1,3}$Department of Mathematics
Kongunadu Arts and Science College
Coimbatore, 641 029, Tamil Nadu, INDIA
$^2$Department of Mathematics
University College of Engineering Nagercoil
(Anna University Constituent College)
Konam, Nagercoil, 629 004, Tamil Nadu, INDIA


Abstract. An $r$-dynamic coloring of a graph $G$ is a proper coloring $c$ of the vertices such that $\left\vert c(N(v))\right\vert \geq min \left\{r, d(v)\right\}$, for each $v\in V(G)$. The $r$-dynamic chromatic number of a graph $G$ is the minimum $k$ such that $G$ has an $r$-dynamic coloring. In this paper, we obtain the $r$-dynamic chromatic number $\left(r=\delta\right)$ of middle, total, central and line graph of fan graphs $F_{1,n}$. The metric relationship between $r$-dynamic chromatic number and $b$-chromatic number of fan graphs are also discussed.

Received: February 15, 2016

AMS Subject Classification: 05C69

Key Words and Phrases: $r$-dynamic coloring, $b$-coloring, fan graph, middle graph, total graph, central graph and line graph

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DOI: 10.12732/ijpam.v106i8.20 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 8
Pages: 169 - 174


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