Determining the b-chromatic number of subdivision-vertex neighbourhood coronas

Abstract

Let G and H be two graphs, each one of them being a path, a cycle or a star. In this paper, we determine the b-chromatic number of every subdivision-vertex neighbourhood corona G ⊡ H or G ⊡ Kn, where Kn is the complete graph of order n. It is also established for those graphs Kn ⊡ G having m-degree not greater than n + 2. All the proofs are accompanied by illustrative examples.

Keywords

• b-chromatic number
• subdivision-vertex neighbourhood corona
• path
• cycle
• star
• complete graph
• primary 05c15