Able群上Cayley图的哈密顿性(英文)

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Able群上Cayley图的哈密顿性(英文)

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- Able群上Cayley图的哈密顿性(英文)
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Issue 1, (2003)
- 作者机构：
  
  新疆大学数学与系统科学学院,新疆,乌鲁木齐,830046
- 作者简介：
- 基金信息：
- DOI：
  CLC： O157.5
- Published：2003
- 稿件说明：
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[1]马合木提·阿合力别克.Able群上Cayley图的哈密顿性(英文)[J].新疆大学学报(自然科学版),2003(01):14-21.

马合木提·阿合力别克. Able群上Cayley图的哈密顿性(英文)[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2003, (1).
[1]马合木提·阿合力别克.Able群上Cayley图的哈密顿性(英文)[J].新疆大学学报(自然科学版),2003(01):14-21. DOI：

马合木提·阿合力别克. Able群上Cayley图的哈密顿性(英文)[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2003, (1). DOI：

摘要

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 .

Abstract

Let G be group and S an inverse-closed generating subset of G not containing the identity element of G The Cayley graph C(G

S) of G is defined to be the graph whose vertices correspond to the elements of G and two vertices x and y in C(G

S) are adjacent if only if x1y∈S. The follwing results are obtained in this paper.\;(i)Each path of length 2 in a connected Cayley graph on a finite abelian group is contained in a hamilmitonian cycle.\;(ii)Each path of length 2 in a connected Cayley graph on a countably infinite abelian group is contained in a two-way hamiltonian path.\;(iii)Connected Cayley graphs on finite abelian groups with girth three are pancyclic.\;(iv)Connected Cayley graphs on countably infinite abelian groups with girth three and degree at least four are pancyclic.

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references

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