%0 Journal Article
%T Graphs on Which a Group of Prime Power Order with a Cyclic MaximalSubgroup Acts Edge-Transitively (II)<br>有循环极大子群的素数幂阶群的作用是边传递的图(II)
%A CHEN Shangdi
%A SHI Xinhua
%A <br>陈尚弟
%A 石新华
%J 系统科学与数学
%D 2008
%I 
%X Let ${\it \Gamma}$ be a finite simple undirected graph with no isolated vertices, $G$ is a subgroup of Aut$({\it \Gamma})$. The graph ${\it \Gamma}$ is said to be $G$-edge transitive if $G$ is transitive on the set of edges of ${\it \Gamma}$. We obtain a complete classification of $G$-edge transitive graphs, when $G$ is a group of prime-power order with a cyclic maximal subgroup. This extends Sander's conclusion. Then ${\it \Gamma}$ is $G$-edge-transitive if and only if ${\it \Gamma}$ is one of following graphs:1)\ $p^mK_{1,p^{n-1-m}}$, $0\leq m\leq n-1$;2)\ $p^mK_{1,p^{n-m}}$, $0\leq m\leq n$;3)\ $p^mK_{p,p^{n-m-1}}$, $0\leq m\leq n-2$;4)\ $p^{n-m}C_{p^m}$, $p^m\geq 3,\ m<n$ ;5)\ $2^{n-2}K_{1,1}$;6)\ $p^{n-1-m}C_{p^m}$, $p^m\geq 3,\ m\leq n-1$;7)\ $2p^{n-m}C_{p^m}$, $p^m\geq 3,\ m\leq n-1$;8)\ $2p^{n-m}K_{1,p^m}$, $0\leq m\leq n$;9)\ $p^{n-m}K_{1,2p^m}$, $0\leq m\leq n$;10)\ $p^{n-m}K_{2,p^m}$, $0< m\leq n$;11)\ $C(2p^{n-m},1,p^m)$;12)\ $p^kC(2p^{m-k},1,p^{n-m})$, $0< k<m$, $0<m\leq n$;13)\ $(t-s,2^m)C\big(\frac{2^{m+1}}{(t-,2^m)},1,2^{n-1-m}\big)$,where $0\leq m\leq n-1$, $2^{n-2}(s-1)\equiv 0 \ ({\rm {\rm mod}} \ 2^m)$,$t\equiv 1 \ ({\rm {\rm mod}} \ 2)$, $s\not\equiv t \ ({\rm {\rm mod}} \ 2^m)$,$1\leq s \leq 2^m$, $1\leq t\leq 2^{n-1}$;14)\ $\bigcup\limits_{i=1}^pC_{p^{n-1}}^i$, where$$C_{p^{n-1}}^i=C_{a_1a_{1+1+(i-1)p^{n-2}]}a_{1+21+(i-1)p^{n-2}]}\cdots a_{1+(p^{n-1}-1)1+(i-1)p^{n-2}]}} \cong C_{p^{n-1}},$$$i=1,2,\cdots,p$;15)\ $\bigcup\limits_{i=1}^2C_{2^{n-1}}^i$, where$$C_{2^{n-1}}^i=C_{a_1a_{1+1+(i-1)(2^{n-2}-1)]}a_{1+21+(i-1)(2^{n-2}-1)]}\cdots a_{1+(2^{n-1}-1)1+(i-1)(2^{n-2}-1)]}}\cong C_{2^{n-1}},$$ $ i=1,2$.
%K Graph
%K automorphism group
%K edge-transitive<br>图
%K 自同构群
%K 边传递
%K 有循环
%K 极大子群
%K 数幂
%K 作用
%K 边传递图
%K MAXIMAL
%K SUBGROUP
%K CYCLIC
%K ORDER
%K POWER
%K PRIME
%K 自同构群
%K 素数
%K 结果
%K 完全分类
%K 边集合
%K 孤立点
%K 无向
%K 有限
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=6AB44A136541D96187E2E9F8273E2DF6&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=38B194292C032A66&sid=119B6C0AA09DE6B9&eid=7737D2F848706113&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=5