The vertex-transitive and edge-transitive tetravalent graphs of square-free order
In this paper, a classification is given for tetravalent graphs of square-free order which are vertex-transitive and edge-transitive. It is shown that such graphs are Cayley graphs, edge-regular metacirculants and covers of some graphs arisen from simple groups \(\mathrm{A}_7\), \(\mathrm{J}_1\) and \(\mathrm{PSL}(2,p)\).
edge-transitive graph vertex-transitive graph arc-transitive graph coset graph automorphism group