The b-Chromatic Number of Cubic Graphs

The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex adjacent to some vertex in all the other color classes. It is proved that with four exceptions, the b-chromatic number of cubic graphs is 4. The exceptions are the Petersen graph, K3,3, the prism over K3, and one more sporadic example on 10 vertices. Key words: chromatic number; b-chromatic number; cubic graph; Petersen graph. AMS subject classification (2000): 05C15

• Type: Journal
• Year: 2010
• Where: GC
• Authors: Marko Jakovac, Sandi Klavzar
• Keywords: Applied Computing, B-chromatic Number, Cubic Graph, GC 2010, Petersen Graph