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

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 $p\equiv 1(\mathrm{mod}4)$, and in this family there is a unique graph for a given order.

This paper has been accepted for publication in SCIENCE CHINA Mathematics

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