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.
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2000 AMS Subject Classification
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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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Francis Raj, S., Gokulnath, M. (2019). b-Coloring of the Mycielskian of Regular Graphs. In: Pal, S., Vijayakumar, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science(), vol 11394. Springer, Cham. https://doi.org/10.1007/978-3-030-11509-8_8
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