Construction of graphs with distinct eigenvalues

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• 作者：Zhenzhen Lou ; Qiongxiang Huang ; ^{huangqx@xju.edu.cn} ; Xueyi Huang
• 关键词：Main eigenvalue ; Controllable graph ; Cospectral graph
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：340
• 期：4
• 页码：607-616
• 全文大小：499 K
• 卷排序：340

文摘

Let GG (resp. GnGn) be the set of connected graphs (resp. with nn vertices) whose eigenvalues are mutually distinct, and G∗G∗ (resp. Gn∗) the set of connected graphs (resp. with nn vertices) whose eigenvalues are mutually distinct and main. Two graphs GG and HH are said to be cospectral if they share the same adjacency spectrum. In this paper, we give a new method to construct infinite families of graphs in GG and G∗G∗. Concretely, given a graph GG in GnGn or Gn∗, the infinite families of GG or G∗G∗ are constructed from GG, and furthermore the spectra of such graphs are also characterized by the spectrum of GG. By the way, we use this method to construct some infinite families of non-isomorphic cospectral graphs, especially, including the graphs in GG and G∗G∗.