Total Graphs Are Laplacian Integral

作     者：David Dolžan Polona Oblak 

作者机构：Department of MathematicsFaculty of Mathematics and Physics University of LjubljanaJadranska 21SI-1000 LjubljanaSlovenia Facultyof Computerand Information ScienceUniversity of Ljubljana Vecna pot 113SI-1000 LjubljanaSlovenia 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2022年第29卷第3期

页      面：427-436页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the financial support from the Slovenian Research Agency(research core funding No.P1-0222) 

主　　题：eigenvalue eigenvector Laplacian matrix total graph Laplacian integral 

摘      要：We prove that the Laplacian matrix of the total graph of a finite commutative ring with identity has integer eigenvalues and present a recursive formula for computing its eigenvalues and *** also prove that the total graph of a finite commutative local ring with identity is super integral and give an example showing that this is not true for arbitrary rings.