Volume no :4, Issue no: 2, June (2016)

International Journal of Applied Mathematics and Machine Learning

THE 1-2-3-EDGE LABELLING AND VERTEX COLOURS

Author's: Mehdi Alaeiyan and Mohammad Reza Farahani
Pages: [119] - [133]
Received Date: December 17, 2015
Submitted by: Jianqiang Gao.
DOI: http://dx.doi.org/10.18642/ijamml_7100121608

Abstract

A labelling of the edges of a graph is called vertex-colouring if the labelled degrees of the vertices yield a proper colouring of the graph. In this paper, we show that such a labelling is possible from the label with numbers of the set for all graphs not containing components with exactly 2 vertices.

Keywords

edge-labelling, vertex-colouring, ordering algorithim, labelling algorithm, complete graph, latest edge, layer.