Tetravalent half-arc-transitive p-graphs
A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let p be a prime. A graph is called a p -graph if it is a Cayley graph of order a power of p. In this paper, a characterization is given of tetravalent edge-transitive p-graphs with p an odd prime. This is then applied to construct infinitely many connected tetravalent half-arc-transitive non-normal p-graphs with p an odd prime, and to initiate an investigation of tetravalent half-arc-transitive non-metacirculant p-graphs with p an odd prime. As by-products, two problems reported in the literature are answered.
KeywordsHalf-arc-transitive graph Cayley graph p-graph
Mathematics Subject Classification05C25 20B25
This work was supported by the National Natural Science Foundation of China (11271029), and the Fundamental Research Funds for the Central Universities (2015JBM110). The author gratefully acknowledges the University of Western Australia for hospitality during his visit in 2014. The author also would like to thank the anonymous referees for the valuable comments and suggestions.
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