Total Graphs Are Laplacian Integral  

作　　者：David Dolžan Polona Oblak 

机构地区：[1]Department of Mathematics,Faculty of Mathematics and Physics University of Ljubljana,Jadranska 21,SI-1000 Ljubljana,Slovenia [2]Facultyof Computerand Information Science,University of Ljubljana Vecna pot 113,SI-1000 Ljubljana,Slovenia

出　　处：《Algebra Colloquium》2022年第3期427-436,共10页代数集刊（英文版）

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

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 eigenvectors.We 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.

关 键 词：EIGENVALUE EIGENVECTOR Laplacian matrix total graph Laplacian integral 

分 类 号：O15[理学—数学]