Constructing graphs with given spectrum and the spectral radius at most 2

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• 作者：Drago&scaron ; Cvetković^a ; ^{ecvetkod@etf.rs} ; Irena M. Jovanović^b ; ^{irenaire@gmail.com}
• 关键词：05C50
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：515
• 期：Complete
• 页码：255-274
• 全文大小：393 K
• 卷排序：515

文摘

Two graphs are cospectral if their spectra coincide. The set of all graphs that are cospectral to a given graph, including the graph by itself, is the cospectral equivalence class of the graph. We say that a graph is determined by its spectrum, or that it is a DS-graph, if it is a unique graph having that spectrum. Given n   reals belonging to the interval [−2,2][−2,2], we want to find all graphs on n vertices having these reals as the eigenvalues of the adjacency matrix. Such graphs are called Smith graphs. Our search is based on solving a system of linear Diophantine equations. We present several results on spectral characterizations of Smith graphs.