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arXiv · 2007.06432

Presentations for Vertex Transitive Graphs

Agelos Georgakopoulos·Matthias Hamann·Alex Wendland
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Abstract

We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex transitive graph. As an intermediate step, we prove that every countably infinite, connected, vertex transitive graph has a perfect matching. Incidentally, we construct an example of a 2-ended cubic vertex transitive graph which is not a Cayley graph, answering a question of Watkins from 1990.

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Agelos Georgakopoulos, Matthias Hamann, Alex Wendland. 2020-07-13. Presentations for Vertex Transitive Graphs. https://arxiv.org/abs/2007.06432

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