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Representing vertex-transitive graphs on groupoids. (English) Zbl 1107.05080
Summary: Vertex-transitive graphs are one of the most favoured classes 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 the conviction that the measure of symmetry by vertex-transitive graphs is as rudimentary as it can be. As a way of completing the story, in a sequel we offer a way of characterising these left loops in terms of transversals of left cosets of subgroups of groups.

MSC:
05C75 Structural characterization of families of graphs
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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