The b-chromatic number of Mycielskian of some graphs

Abstract

A b-colouring of a graph G is a proper colouring of the vertices of G such that there exists a vertex in each colour class joined to at least one vertex in each other colour classes. The b-chromatic number of a graph G, denoted by φ(G) is the largest integer k such that G has a b-colouring with k colours. The Mycielskian or Mycielski graph µ(H) of a graph H with vertex set {v 1 , v 2 , …, v n } is a graph G obtained from H by adding n + 1 new vertices {u, u 1 , u 2 , …, u n }, joining u to each vertex u i (1 ≤ i ≤ n) and joining u i to each neighbour of v i in H. In this paper, we obtain the b-chromatic number of Mycielskian of paths, complete graphs, complete bipartite graphs and wheels. . Her areas of interests are graph theory and fuzzy graph theory. She has more than 50 research publications and published seven books in the field of fuzzy graph theory. She has guided 11 research scholars in the Department of Mathematics NIT Calicut, among them seven scholars got awarded PhD and four are ongoing. This paper is a revised and expanded version of a paper entitled 'The b-chromatic number of Mycielskian of paths' presented at International