IJPAM: Volume 106, No. 8 (2016)

THE STABLE B-CHROMATIC GRAPHS

A. Jeeva$^1$, R. Selvakumar$^2$, M. Nalliah$^3$
$^{1,2,3}$School of Advanced Sciences
VIT University
Vellore, 632014, INDIA


Abstract. A $ b$-coloring is a proper $k$-coloring of the vertices of a graph such that each color class has a vertex that is adjacent to a vertex of every other color class. The $ b$-chromatic number of a graph $G$ is the largest integer $k$ such that $G$ admits a $ b$-coloring with $k$ colors. A graph $G$ is said to be stable $ b$-chromatic graph if $b(G.uv)=b(G)$ for every $u,v\in V(G)$ with $u$ is adjacent to $v$. In this paper we obtain some basic properties of $b_s$-chromatic graphs.

Received: February 15, 2016

AMS Subject Classification: 05C15

Key Words and Phrases: b-coloring, b-chromatic number, b-system, b$_{s}$-chromatic graphs

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DOI: 10.12732/ijpam.v106i8.2 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: 7 - 12


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