IJSRSET calls volunteers interested to contribute towards the scientific development in the field of Science, Engineering and Technology

Home > IJSRSET173659                                                     

Study of b-Chromatic Number of Wheel Graph


Karthiga Gayathri K, Naveen L
  • Abstract
  • Authors
  • Keywords
  • References
  • Details
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.

Karthiga Gayathri K, Naveen L

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

  1. Francis Raj S. and Balakrishnan R.,"Bounds for the b-chromatic num-ber of theMycielskianof some families of graphs", to appear in ArsCombi-natoria.
  2. Harary F. and Norman R. Z., "Some properties of line digraphs", Ren-diconti delCircoloMathematico di Palermo, 9(1960) pp.161-168.
  3. Hemminger L. and Beineke L. W., "Line graphs and line digraphs".
  4. J.A Boncly and V.S.R murthy graph theory with application.
  5. The b-Chromatic Number of Central Graph of Some Special Graphs.," Jethruth Emelda Maryl1 and Kavithaa"

Publication Details

Published in : Volume 3 | Issue 6 | September-October - 2017
Date of Publication Print ISSN Online ISSN
2017-10-31 2395-1990 2394-4099
Page(s) Manuscript Number   Publisher
242-245 IJSRSET173659   Technoscience Academy

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.
URL : http://ijsrset.com/IJSRSET173659.php