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 .
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.
出处
《新疆大学学报（自然科学版）》
CAS
2003年第1期14-21,共8页
Journal of Xinjiang University(Natural Science Edition)
