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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Symmetry in Cayley graphs
凯莱图 对称性 图论
2023/4/27
Cayley graphs form an important class of vertex-transitive graphs, which have been the object of study for many decades. These graphs admit a group of automorphisms that acts regularly (sharply-transi...
We prove that if Cay(G; S) is a connected Cayley graph with n vertices, and the prime factorization of n is very small, then Cay(G; S) has a hamiltonian cycle. More precisely, if p, q, and r are disti...
Cayley图的Hamilton性的若干问题
群的数量性质；表代数；Cayley图
2008/4/25
利用群中"元的阶之集"以及"群的阶"这两个数量集来统一刻画所有的单群，又完成了两类半李型单群$^2A_n$, $^2D_n(q)$，$D_n(q)$（$n$为奇）和$C_2(q)$的刻画. 仅用"元的阶之集"（或谱）对系列的单群$F_4(2^m)$,拟单群$PGL(2,p)$以及特殊的单群进行了刻画. 将有限群的数量刻画扩展到利用特征标次数的集合来研究有限群的结构. 完成了一个次数是3的非实基元生...