Study of b-Chromatic Number of Wheel Graph

Authors(2) :-Karthiga Gayathri K, Naveen L

In this paper we have generalized some of basic result on chromatic number.The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex that has a neighbor in each of the other color classes. All graph considered here are simple, undirected and finite. For a graph G, we denote by V(G)its vertex set and by E(G)its edge set;|V(G)|is the order and x(G)is the chromatic number of G. for a graph G and a vertex x of G. Let G=(V,E) be an undirected and loopless graph.The b-chromatic number of a graph G is the largest iteger k such that G admits a proper k-colouring in which every colour class contains atleast one vertex adjacent to some vertex in all the other colour classes. A proper k-colouring of a graph G=(V(G),E(G)) is a mapping f:V(G)->N such that every two adjacent vertices receive different colors. The chromatic number of a graph G is denoted by X(G), is the minimum number foe which G has a proper k-colouring. The set of vertices with a specific colour is called a colour class. The b-chromatic number ?(G)is the largest integer k such that G admits a b-colouring with k colour.

Authors and Affiliations

Karthiga Gayathri K
P.G. Student, Department of Mathematics Dr.SNS Rajalakshmi College of Arts &Science (Autonomous), Coimbatore, Tamilnadu, India
Naveen L
Assistant Professor Dr.SNS Rajalakshmi College of Arts &Science (Autonomous), Coimbatore, Tamilnadu, India

b-Chromatic Number, Line Graph, Wheel Graph, Complete Graph and Line Graph of a Wheel Graph

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Publication Details

Published in : Volume 3 | Issue 6 | September-October 2017
Date of Publication : 2017-10-31
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 242-245
Manuscript Number : IJSRSET173659
Publisher : Technoscience Academy

Print ISSN : 2395-1990, Online ISSN : 2394-4099

Cite This Article :

Karthiga Gayathri K, Naveen L, " Study of b-Chromatic Number of Wheel Graph, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 3, Issue 6, pp.242-245, September-October-2017.
Journal URL : http://ijsrset.com/IJSRSET173659

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