Let Γ be a finite connected locally primitive Cayley graph of an abelian group.It is shown that one of the following holds:(1) Γ = Kn,Kn,n,Kn,n-nK2,Kn ×···× Kn;(2) Γ is the standard double ...Let Γ be a finite connected locally primitive Cayley graph of an abelian group.It is shown that one of the following holds:(1) Γ = Kn,Kn,n,Kn,n-nK2,Kn ×···× Kn;(2) Γ is the standard double cover of Kn ×···× Kn ;(3) Γ is a normal or a bi-normal Cayley graph of an elementary abelian or a meta-abelian 2-group.展开更多
We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p, where p is a prime number. As a consequence we prove if IGI = 25p, δ = 0, 1, 2 and p prime, then F 1 Cay（G, S） i...We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p, where p is a prime number. As a consequence we prove if IGI = 25p, δ = 0, 1, 2 and p prime, then F 1 Cay（G, S） is a connected normal 1/2 arc-transitive Cayley graph only if G = F4p, where S is an inverse closed generating subset of G which does not contain the identity element of G and F4p is a group with presentation F4p = （a, b ｜aP = b4 = 1, b-lab = a^λ）, where λ2 = -1 （mod p）.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10771132,11071210)Australia Research Council Discovery Grant
文摘Let Γ be a finite connected locally primitive Cayley graph of an abelian group.It is shown that one of the following holds:(1) Γ = Kn,Kn,n,Kn,n-nK2,Kn ×···× Kn;(2) Γ is the standard double cover of Kn ×···× Kn ;(3) Γ is a normal or a bi-normal Cayley graph of an elementary abelian or a meta-abelian 2-group.
文摘We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p, where p is a prime number. As a consequence we prove if IGI = 25p, δ = 0, 1, 2 and p prime, then F 1 Cay（G, S） is a connected normal 1/2 arc-transitive Cayley graph only if G = F4p, where S is an inverse closed generating subset of G which does not contain the identity element of G and F4p is a group with presentation F4p = （a, b ｜aP = b4 = 1, b-lab = a^λ）, where λ2 = -1 （mod p）.
