On the spectra of strong power graphs of finite groups
Received:October 11, 2018  Revised:January 22, 2019
Key Word: Strong power graph   cyclic group   characteristic polynomial   spectrum  
Fund ProjectL:The National Natural Science Foundation of China (Grant No. 11801441) and the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 18JK0623).
Author NameAffiliationE-mail
Ruiqin Fu Xi'
'
an Shiyou University 
xuanlma@mail.bnu.edu.cn 
Xuanlong Ma Xi'
'
an Shiyou University 
xuanlma@mail.bnu.edu.cn 
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Abstract:
      Let $G$ be a finite group of order $n$. The strong power graph of $G$ is the undirected graph whose vertex set is $G$ and two distinct vertices $x$ and $y$ are adjacent if $x^{n_1}=y^{n_2}$ for some positive integers $n_1,n_2 < n$. In this paper, we give the characteristic polynomials of the distance and adjacency matrix of the strong power graph of $G$, and compute its distance and adjacency spectrum.
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