Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, ...Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111： 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30： 103-110].展开更多
In this paper we propose the concept of generalized semi-Cayley graphs, which is a combination of semi-Cayley graphs and generalized Cayley graphs. We study the isomorphisms and automorphisms of generalized semi-Cayle...In this paper we propose the concept of generalized semi-Cayley graphs, which is a combination of semi-Cayley graphs and generalized Cayley graphs. We study the isomorphisms and automorphisms of generalized semi-Cayley graphs and other related properties.展开更多
Let G be a finite group, and S a subset of G1 with S=S-1. We use X=Cay(G,S) to denote the Cayley graph of G with respect to S. We call S a CI-subset of G, if for any isomorphism Cay(G,S)Cay(G,T) there is an α∈Aut(G)...Let G be a finite group, and S a subset of G1 with S=S-1. We use X=Cay(G,S) to denote the Cayley graph of G with respect to S. We call S a CI-subset of G, if for any isomorphism Cay(G,S)Cay(G,T) there is an α∈Aut(G) such that Sα=T. Assume that m is a positive integer. G is called an m-CI-group if every subset S of G with S=S-1 and |S|≤m is CI. In this paper we prove that the alternating group A5 is a 4-CI-group, which was a conjecture posed by Li and Praeger.展开更多
一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类...一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类二元生成子集的4-度C ay ley图的正规性与正则性,解决了4-度C ay ley图的完全分类问题.展开更多
基金Acknowledgements The first author was supported by the Natural Science Foundation of China （Grant No. 11301254）, the Natural Science Foundation of Henan Province （Grant No. 132300410313）, and the Natural Science Foundation of Education Bureau of Henan Province （Grant No. 13A110800）. The second author was supported by the National Natural Science Foundation of China （Grant No. 11171129） and the Doctoral Fund of Ministry of Education of China （Grant No. 20130144110001）.
文摘Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111： 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30： 103-110].
文摘In this paper we propose the concept of generalized semi-Cayley graphs, which is a combination of semi-Cayley graphs and generalized Cayley graphs. We study the isomorphisms and automorphisms of generalized semi-Cayley graphs and other related properties.
基金the National Natural Science Foundation of China (Grant Nos. 19831050 and69873002) and the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 97000141) , and also by Korea Science and Engineering Foundation (Grant No. K
文摘Let G be a finite group, and S a subset of G1 with S=S-1. We use X=Cay(G,S) to denote the Cayley graph of G with respect to S. We call S a CI-subset of G, if for any isomorphism Cay(G,S)Cay(G,T) there is an α∈Aut(G) such that Sα=T. Assume that m is a positive integer. G is called an m-CI-group if every subset S of G with S=S-1 and |S|≤m is CI. In this paper we prove that the alternating group A5 is a 4-CI-group, which was a conjecture posed by Li and Praeger.
文摘一个有限群称为广义四元数群,若Q4n=〈a,b a2n=1,b2=an,ab=a-1,〉n 3.本文根据广义四元数群Q4p(p为奇素数)中只有两类二元生成子集,且它们在Aut(Q4p)的作用下是传递的.结合具体图形,利用查圈的方法重点地证明了广义四元数群关于这两类二元生成子集的4-度C ay ley图的正规性与正则性,解决了4-度C ay ley图的完全分类问题.
