Abstract
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 \(\mathrm{PSL}(2,p)\).
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The work was supported by the NSFC and an ARC Discovery Project Grant.
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Li, C.H., Lu, Z.P. & Wang, G.X. The vertex-transitive and edge-transitive tetravalent graphs of square-free order. J Algebr Comb 42, 25–50 (2015). https://doi.org/10.1007/s10801-014-0572-z
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DOI: https://doi.org/10.1007/s10801-014-0572-z