Smith forms for adjacency matrices of circulant graphs

被引：9
|
作者：
Williams, Gerald [1 ]
机构：
[1] Univ Essex, Dept Math Sci, Colchester CO4 3SQ, Essex, England
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 443卷
关键词：
Smith normal form; Circulant graph; Adjacency matrix; EIGENVALUES;
D O I：
10.1016/j.laa.2013.11.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We calculate the Smith normal form of the adjacency matrix of each of the following graphs or their complements (or both): complete graph, cycle graph, square of the cycle, power graph of the cycle, distance matrix graph of cycle, Andrasfai graph, Doob graph, cocktail party graph, crown graph, prism graph, Mobius ladder. The proofs operate by finding the abelianization of a cyclically presented group whose relation matrix is column equivalent to the required adjacency matrix. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：21 / 33
页数：13
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