Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results a...Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut（Г） contains a subgroup G of order pq that acts edge-transitively on F, then F is one of the following graphs： （1） pK1,1; （2） pqK1,1; （3） pgq,1; （4） qKp,1 （p 〉 q）; （5） pCq （q 〉 2）; （6） qCp （p 〉 q）; （7） Cp （p 〉 q = 2）; （8） Cpq; （9） （Zp, C） whereC={±r^μ ｜μ∈Zq} withq〉2, q｜（p-1） and r≠1≡r^q （modp）; （10） Kp,1 （p 〉 q）; （11） a double Cayley graph B（G,C） with C = {1-r^μ ｜ μ ∈ Zq} and r≠1≡r^q （modp）; （12） Kpq,1;or （13） Kp,q.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
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
A graph F is called G-locally-quasiprimitive if each normal subgroup of Gv acts on F（v） trivially or transitively for every vertex v. In this paper we analyse the global action and the structural information of such...A graph F is called G-locally-quasiprimitive if each normal subgroup of Gv acts on F（v） trivially or transitively for every vertex v. In this paper we analyse the global action and the structural information of such groups G, extending the previous results for locally-primitive graphs and vertex-transitive locally-quasiprimitive graphs.展开更多
基金Supported by the NNSF of China (60776810,10871205)the NSF of Tianjin (08JCYBJC13900)the KYS of CAUC (09CAUC-S02)
文摘Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut（Г） contains a subgroup G of order pq that acts edge-transitively on F, then F is one of the following graphs： （1） pK1,1; （2） pqK1,1; （3） pgq,1; （4） qKp,1 （p 〉 q）; （5） pCq （q 〉 2）; （6） qCp （p 〉 q）; （7） Cp （p 〉 q = 2）; （8） Cpq; （9） （Zp, C） whereC={±r^μ ｜μ∈Zq} withq〉2, q｜（p-1） and r≠1≡r^q （modp）; （10） Kp,1 （p 〉 q）; （11） a double Cayley graph B（G,C） with C = {1-r^μ ｜ μ ∈ Zq} and r≠1≡r^q （modp）; （12） Kpq,1;or （13） Kp,q.
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.
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.
文摘A graph F is called G-locally-quasiprimitive if each normal subgroup of Gv acts on F（v） trivially or transitively for every vertex v. In this paper we analyse the global action and the structural information of such groups G, extending the previous results for locally-primitive graphs and vertex-transitive locally-quasiprimitive graphs.
