Which finitely generated Abelian groups admit isomorphic Cayley graphs?

被引：4
作者：
Loeh, Clara [1 ]
机构：
[1] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany
来源：
GEOMETRIAE DEDICATA | 2013年 / 164卷 / 01期
关键词：
Cayley graphs; Graph isomorphisms; Rigidity;
D O I：
10.1007/s10711-012-9761-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that Cayley graphs of finitely generated Abelian groups are rather rigid. As a consequence we obtain that two finitely generated Abelian groups admit isomorphic Cayley graphs if and only if they have the same rank and their torsion parts have the same cardinality. The proof uses only elementary arguments and is formulated in a geometric language.
引用
收藏
页码：97 / 111
页数：15
相关论文
共 6 条
[1]  
[Anonymous], CAYLEY GRAPHS FINITE
[2]  
de la Harpe P., 2000, Chicago Lectures in Mathematics
[3]  
Elspas B., 1970, J COMBINATORIAL THEO, V9, P297, DOI DOI 10.1016/S0021-9800(70)80068-0
[4]   On isomorphisms of finite Cayley graphs - a survey [J].
Li, CH .
DISCRETE MATHEMATICS, 2002, 256 (1-2) :301-334
[5]   Digraphical regular representations of infinite finitely generated groups [J].
Moller, RG ;
Seifter, N .
EUROPEAN JOURNAL OF COMBINATORICS, 1998, 19 (05) :597-602
[6]   Isomorphisms of Cayley graphs of a free abelian group [J].
Ryabchenko, A. A. .
SIBERIAN MATHEMATICAL JOURNAL, 2007, 48 (05) :919-922
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