Edge colouring by total labellings

We introduce the concept of an edge-colouring total k-labelling. This is a labelling of the vertices and the edges of a graph G with labels 1, 2, . . . , k such that the weights of the edges define a proper edge colouring of G. Here the weight of an edge is the sum of its label and the labels of its two endvertices. We define t(G) to be the smallest integer k for which G has an edge-colouring total k-labelling. This parameter has natural upper and lower bounds in terms of the maximum degree of G: ( + 1)/2

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Stephan Brandt, Kristína Budajová, Dieter Rautenbach, Michael Stiebitz
• Keywords: DM 2010, Edge-colouring Total, Labels, Proper Edge