Integral Cayley Graphs

被引：0

作者：

W. Guo

D. V. Lytkina

V. D. Mazurov

D. O. Revin

机构：

[1] University of Science and Technology of China,

[2] Siberian State University of Telecommunications and Information Sciences,undefined

[3] Novosibirsk State University,undefined

[4] Sobolev Institute of Mathematics,undefined

来源：

Algebra and Logic | 2019年 / 58卷

关键词：

Cayley graph; adjacency matrix of graph; spectrum of graph; integral graph; complex group algebra; character of group;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let G be a group and S ⊆ G a subset such that S = S−1, where S−1 = {s−1 | s ∈ S}. Then a Cayley graph Cay(G, S) is an undirected graph Γ with vertex set V (Γ) = G and edge set E(Γ) = {(g, gs) | g ∈ G, s ∈ S}. For a normal subset S of a finite group G such that s ∈ S ⇒ sk ∈ S for every k ∈ ℤ which is coprime to the order of s, we prove that all eigenvalues of the adjacency matrix of Cay(G, S) are integers. Using this fact, we give affirmative answers to Questions 19.50(a) and 19.50(b) in the Kourovka Notebook.

引用

页码：297 / 305

页数：8