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arXiv · 1603.05851

Vertex-transitive Haar graphs that are not Cayley graphs

Marston Conder·István Estélyi·Tomaž Pisanski
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Abstract

In a recent paper (arXiv:1505.01475 ) Estélyi and Pisanski raised a question whether there exist vertex-transitive Haar graphs that are not Cayley graphs. In this note we construct an infinite family of trivalent Haar graphs that are vertex-transitive but non-Cayley. The smallest example has 40 vertices and is the well-known Kronecker cover over the dodecahedron graph $G(10,2)$, occurring as the graph $40$ in the Foster census of connected symmetric trivalent graphs.

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Marston Conder, István Estélyi, Tomaž Pisanski. 2016-03-18. Vertex-transitive Haar graphs that are not Cayley graphs. https://arxiv.org/abs/1603.05851

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