On the image-labelling of graphs Original Research Article

The image-labelling of graphs, is a graph theoretic framework introduced by Griggs and Yeh [Labelling graphs with a condition at distance 2, SIAM J. Discrete Math. 5 (1992) 586–595] to model the channel assignment problem. In this paper we improve the best known upper bound for the image-labelling of graphs with given maximum degree. We show that for any integer image, any graph G with maximum degree image admits an image-labelling such that the labels range from 0 to image.