Representing vertex-transitive graphs on groupoids

Abstract

Vertex-transitive graphs are one of the most favoured class of graphs in modelling scientific phenomena if symmetry is at issue. An understanding of these graphs should, therefore, be an obvious undertaking. Here, we present a characterisation of vertex-transitive graphs as left loop graphs and expose the measure of symmetry in terms of the richness of the algebraic systems that represent them. In so doing, we hope to offer a conviction that vertex-transitive graphs measure of symmetry is as rudimentary as can be.