马合木提·阿合力别克

• 1:新疆大学数学与系统科学学院 新疆乌鲁木齐830046

摘要(Abstract)：

设 G是群 ,S是 G的不含单位元的子集 ,满足 S=S1 ,G的相对于 S的 Cayley图 ,是一个以 G为顶点集的无向图 ,对 G的任意两上元 x和 y,x和 y在 C( G,S)中相邻 ,当且今当 x1 y∈ S.本文中我们得到了以下结论 :( i)设 G是阶至少为 2的有限 Abel群 .S G\{ 0 }且 S=S1 ,则 C( G,S)中每个二长路都包含在一个哈密顿圈中 .( ii)设 G是可数无限 Abel群 ,S G\{ 0 }满足 S=S1 和 | S|≥ 4 .则 C( G,S)中每个长为 2的路含在一条双向哈密顿路上 .( iii)有限 Abel群上围长为 3,阶数至少为 3的连通 Cayley图是泛圈的 .( iv)设 G是可数无限 Abel群 ,S G\{ 0 }满足 S=S1和 | S|≥ 4 .若 girth[C( G,S) ]=3,则 C( G,S)是泛圈的 .

关键词(KeyWords)： Cayley图;Abel群;Pancycli

Abstract:

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基金项目(Foundation):

作者(Author): 马合木提·阿合力别克

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