$b$-Chromatic number of Some Splitting Graphs

S. Arockiaraj, V. Premalatha


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 $C_n\circ K_1$.


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

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S. Arockiaraj, P. Mahalakshmi and P. Namasivayam, Odd sum labeling on splitting graphs, Util. Math. (accepted).

N. Alon and B. Mohar, The chromatic number of graph power, Combinatorics Probability and Computing, 11 (1993), 1–10.

I. W. Irving and D. F. Manlove The b-chromatic number of a graph, Discrete Appl. Math., 91 (1999), 127–141.

J. Kratochvil, Zs. Tuza and M. Voigt, On the $b$-chromatic number of graphs, Lecturer Notes in Computer Science, Springer, Berlin, 2573 (2002), 310–320.

M. Kouider, b-chromatic number of a graph, subgraphs, degrees, Res. Rep. 1392, LRI, Univ. Orsay, France, 2004.

R. Javedi and B. Omoomi, On b-coloring of Cartesian product of graphs, Ars Combin., 107 (2012), 521–536.

E. Sampathkumar and H.B. Walikar, On splitting graph of a graph, J. Karnatak Univ. Sci., 25(13) (1980), 13–16.

K. Thilagavathi, D. Vijayalakshmi and N. Roopesh, b-coloring of central graphs, International Journal of Computer Applications, 3(11) (2010), 27–29.

Vivin. J. Vernold and M. Venkatachalam, The b-chromatic number of corona graphs, Util. Math., 88 (2012), 299–307.

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

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