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arXiv · 1705.04551

Cubic vertex-transitive non-Cayley graphs of order 12p

Wei-Juan Zhang·Yan-Quan Feng·Jin-Xin Zhou
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Abstract

A graph is said to be {\em vertex-transitive non-Cayley} if its full automorphism group acts transitively on its vertices and contains no subgroups acting regularly on its vertices. In this paper, a complete classification of cubic vertex-transitive non-Cayley graphs of order $12p$, where $p$ is a prime, is given. As a result, there are $11$ sporadic and one infinite family of such graphs, of which the sporadic ones occur when $p=5$, $7$ or $17$, and the infinite family exists if and only if $p\equiv1\ (\mod 4)$, and in this family there is a unique graph for a given order.

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Wei-Juan Zhang, Yan-Quan Feng, Jin-Xin Zhou. 2017-05-12. Cubic vertex-transitive non-Cayley graphs of order 12p. https://arxiv.org/abs/1705.04551

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