Vertex-transitive Haar graphs that are not Cayley graphs
Group Theory
2016-03-21 v1 Combinatorics
Abstract
In a recent paper (arXiv:1505.01475 ) Est\'elyi 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 , occurring as the graph in the Foster census of connected symmetric trivalent graphs.
Keywords
Cite
@article{arxiv.1603.05851,
title = {Vertex-transitive Haar graphs that are not Cayley graphs},
author = {Marston Conder and István Estélyi and Tomaž Pisanski},
journal= {arXiv preprint arXiv:1603.05851},
year = {2016}
}
Comments
9 pages, 2 figures