B-Chromatic Number of some Cycle Related Graphs
Samir K. VAIDYA, M. S. Shukla · International Journal of Mathematics and Soft Computing · 2014
A b-coloring by k-colors is a proper coloring of the vertices of graph G such that in each color classes there exists a vertex that has neighbours in all the other k-1 color classes. The b-chromatic number Phi(G) is the largest integer k for which G admits a b-coloring with k-colors. If chi(G) is the chromatic number of G then G is said to be b-continuous if b-coloring exists for every integer k satisfying Chi(G) less than or equal to k which is less than or equl to Phi(G). We investigate the b-chromatic number of some cycle related graphs and also discuss their b-continuity.