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b-Coloring of the Mycielskian of Regular Graphs

  • S. Francis RajEmail author
  • M. Gokulnath
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)

Abstract

The b-chromatic number b(G) of a graph G is the maximum k for which G has a proper vertex coloring using k colors such that each color class contains at least one vertex adjacent to a vertex of every other color class. In this paper, we have mainly investigated on the b-chromatic number of the Mycielskian of regular graphs. In particular, we have obtained the exact value of the b-chromatic number of the Mycielskian of some classes of graphs. This includes a few families of regular graphs, graphs with \(b(G)=2\) and split graphs. In addition, we have found bounds for the b-chromatic number of the Mycielskian of some more families of regular graphs in terms of the b-chromatic number of their original graphs.

Keywords

b-coloring b-chromatic number Mycielskian of graphs Regular graphs 

2000 AMS Subject Classification

05C15 

Notes

Acknowledgment

For the first author, this research was supported by SERB DST Project, Government of India, File no: EMR/2016/007339. For the second author, this research was supported by UGC - BSR, Research Fellowship, Government of India.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsPondicherry UniversityPuducherryIndia

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