A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric g...A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2 for an odd prime p.展开更多
Let G be a finite group, and S be a subset of G. The bi-Cayley graph BCay（G, S） of G with respect to S is defined as the bipartite graph with vertex set G x {0,1} and edge set {（g,0）, （gs, 1）1 g ε G, s εS}. In...Let G be a finite group, and S be a subset of G. The bi-Cayley graph BCay（G, S） of G with respect to S is defined as the bipartite graph with vertex set G x {0,1} and edge set {（g,0）, （gs, 1）1 g ε G, s εS}. In this paper, we first provide two interesting results for edge-hamiltonian property of Cayley graphs and bi-Cayley graphs. Next, we investigate the edge^hamiltonian property of F = BCay（G, S）, and prove that F is hamiltonian if and only if F is edge-hamiltonian when F is a connected bi-Cayley graph.展开更多
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
In this paper, we investigate semisymmetric graphs of order 6p2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p2, and then, on the basis of the clas...In this paper, we investigate semisymmetric graphs of order 6p2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p2, and then, on the basis of the classification result, we prove that, for primes k and p, a connected graph Γ of order 6p2 and valency k is semisymmetric if and only if k = 3 and either Γ is the Gray graph, or p ≡ 1 (mod 6) and Γ is isomorphic to one known graph.展开更多
Let p be a prime.In this paper,a complete classification of edge-transitive N-covers of a cubic symmetric graph of order 2p is given for the case when N is a twogenerator 2-group whose derived subgroup is either isomo...Let p be a prime.In this paper,a complete classification of edge-transitive N-covers of a cubic symmetric graph of order 2p is given for the case when N is a twogenerator 2-group whose derived subgroup is either isomorphic to Z_(2)^(3)or generated by at most two elements.As an application,it is shown that 11 is the smallest value of n for which there exist infinitely many cubic semisymmetric graphs with order of the form 2^(n)p.展开更多
基金This work was supported partly by the National Natural Science Foundation of China(Grant Nos.19831050,10171006)the Doctoral Program Foundation of Institutions of Higher Education of China(Grant No.2000000102).
文摘A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2 for an odd prime p.
基金partially supported by the NSFC(No.11171368)the Scientific Research Foundation for Ph.D of Henan Normal University(No.qd14143 and No.qd14142)
文摘Let G be a finite group, and S be a subset of G. The bi-Cayley graph BCay（G, S） of G with respect to S is defined as the bipartite graph with vertex set G x {0,1} and edge set {（g,0）, （gs, 1）1 g ε G, s εS}. In this paper, we first provide two interesting results for edge-hamiltonian property of Cayley graphs and bi-Cayley graphs. Next, we investigate the edge^hamiltonian property of F = BCay（G, S）, and prove that F is hamiltonian if and only if F is edge-hamiltonian when F is a connected bi-Cayley graph.
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.
文摘In this paper, we investigate semisymmetric graphs of order 6p2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p2, and then, on the basis of the classification result, we prove that, for primes k and p, a connected graph Γ of order 6p2 and valency k is semisymmetric if and only if k = 3 and either Γ is the Gray graph, or p ≡ 1 (mod 6) and Γ is isomorphic to one known graph.
基金supported by the Fundamental Research Funds for the Central Universities(2020YJS190)the National Natural Science Foundation of China(12071023,11671030)。
文摘Let p be a prime.In this paper,a complete classification of edge-transitive N-covers of a cubic symmetric graph of order 2p is given for the case when N is a twogenerator 2-group whose derived subgroup is either isomorphic to Z_(2)^(3)or generated by at most two elements.As an application,it is shown that 11 is the smallest value of n for which there exist infinitely many cubic semisymmetric graphs with order of the form 2^(n)p.
基金Supported by the National Natural Science Foundation of China(11201201)the Natural Science Foundation of Gansu Province(1308RJZA112)the Fundamental Research Funds for the Central Universities(lzujbky-2015-76)
