$b$-Chromatic number of Some Splitting Graphs

S. Arockiaraj, V. Premalatha

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 $C_n\circ K_1$.

Keywords


$b$-colouring; $b$-chromatic number

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v7i1.266

eISSN 0975-5748; pISSN 0974-875X