$b$-Chromatic number of Some Splitting Graphs

Authors

  • S. Arockiaraj Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi- 626 005, Tamilnadu
  • V. Premalatha Department of Mathematics, Karpagam University, Coimbatore, Tamilnadu

DOI:

https://doi.org/10.26713/jims.v7i1.266

Keywords:

$b$-colouring, $b$-chromatic number

Abstract

A $b$-colouring of a graph $G$ is a proper vertex colouring of $G$ such that each colour class contains a vertex that has atleast one neighbour in every other colour class and $b$-chromatic number of a graph $G$ is the largest integer $\phi(G)$ for which $G$ has a $b$-colouring with $\phi(G)$ colours. In this paper, we have obtained the $b$-chromatic number of the splitting graphs of path $P_n$, cycle $C_n$, star $K_{1,n}$, fan graph $F_n$, triangular snake $T_n$, the $H$-graph $H_n$, the corona graph $P_n\circ K_1$ and $C_n\circ K_1$.

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References

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Published

2015-06-30
CITATION

How to Cite

Arockiaraj, S., & Premalatha, V. (2015). $b$-Chromatic number of Some Splitting Graphs. Journal of Informatics and Mathematical Sciences, 7(1), 49–67. https://doi.org/10.26713/jims.v7i1.266

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Section

Research Articles