IJPAM: Volume 119, No. 4 (2018)

Title

DOMINATOR AND STRONG DOMINATOR
CHROMATIC NUMBER OF PRODUCT GRAPHS

Authors

R. Kalaivani$^1$, D. Vijayalakshmi$^2$
$^{1,2}$Department of Mathematics
Kongunadu Arts and Science College
Coimbatore, 641 031, INDIA

Abstract

A dominator coloring of a graph $G$ is a proper coloring of $G$ in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of $G$ is called the dominator chromatic number of $G$ and is denoted by $\chi_d(G)$. Let $G = (V, E)$ be a simple graph. A proper color partition of $V (G)$ is called a strong dominator coloring, if the vertex $v$ strongly dominates $u$ then $deg(v) \geq deg(u)$. In this paper, we obtain the strong dominator chromatic number for the tensor product of $ K_{m}\tens K_{n}$, and $ P_m \tens K_{1,n}$ respectively. Also upper bound and lower bound for the the dominator chromatic number of modular product graphs are discussed.

History

Received: September 18, 2017
Revised: August 10, 2018
Published: August 10, 2018

AMS Classification, Key Words

AMS Subject Classification: 05C15
Key Words and Phrases: coloring, domination, dominator coloring, strong dominator coloring, tensor product

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How to Cite?

DOI: 10.12732/ijpam.v119i4.10 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: 2018
Volume: 119
Issue: 4
Pages: 685 - 693


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