Strongly self-dual graphs

被引：15

作者：

Tifenbach, R. M. ^{[1
]}

机构：

[1] Natl Univ Ireland Maynooth, Hamilton Inst, Maynooth, Kildare, Ireland

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 12期

关键词：

Adjacency matrix; Dual graph; Inverse graph; Unique perfect matching;

D O I：

10.1016/j.laa.2011.05.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a class of graphs whose adjacency matrices are nonsingular with integral inverses, denoted h-graphs. lithe h-graphs G and H with adjacency matrices M(G) and M(H) satisfy M(G)(-1) = SM(H)S, where S is a signature matrix, we refer to H as the dual of G. The dual is a type of graph inverse. If the h-graph G is isomorphic to its dual via a particular isomorphism, we refer to G as strongly self-dual. We investigate the structural and spectral properties of strongly self-dual graphs, with a particular emphasis on identifying when such a graph has 1 as an eigenvalue. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：3151 / 3167

页数：17

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