A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive.Let p be a prime.By Folkman[J.Combin.Theory 3(1967),215–232],there is no cubic semisymmetric graph of order 2p or 2p^2,and by...A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive.Let p be a prime.By Folkman[J.Combin.Theory 3(1967),215–232],there is no cubic semisymmetric graph of order 2p or 2p^2,and by Hua et al.[Science in China A 54(2011),1937–1949],there is no cubic semisymmetric graph of order 4p^2.Lu et al.[Science in China A 47(2004),11–17]classified connected cubic semisymmetric graphs of order 6p^2.In this paper,for p>q≥5 two distinct odd primes,it is shown that the sufficient and necessary conditions which a connected cubic edge transitive bipartite graph of order 2qp^2 is semisymmetric.展开更多
基金Supported by the National Natural Science Foundation of China(Nos.11301159,11671030,11601132,11501176)the Education Department of Henan Science and Technology Research Key Project(No.13A110543)
文摘A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive.Let p be a prime.By Folkman[J.Combin.Theory 3(1967),215–232],there is no cubic semisymmetric graph of order 2p or 2p^2,and by Hua et al.[Science in China A 54(2011),1937–1949],there is no cubic semisymmetric graph of order 4p^2.Lu et al.[Science in China A 47(2004),11–17]classified connected cubic semisymmetric graphs of order 6p^2.In this paper,for p>q≥5 two distinct odd primes,it is shown that the sufficient and necessary conditions which a connected cubic edge transitive bipartite graph of order 2qp^2 is semisymmetric.
