The Spectral Properties of p-Sombor(Laplacian)Matrix of Graphs  

作　　者：Hechao LIU Lihua YOU 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangdong 510631,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第3期277-288,共12页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos.11971180;12271337);the Characteristic Innovation Project of General Colleges and Universities in Guangdong Province (Grant No.2022KTSC X225)。

摘　　要：The Sombor index,which was recently introduced into chemical graph theory,can predict physico-chemical properties of molecules.In this paper,we investigate the properties of (p-)Sombor index from an algebraic viewpoint.The p-Sombor matrix Sp(G) is the square matrix of order n whose (i,j)-entry is equal to ((di)^(p)+(dj)^(p))^(1/p)if vi~vj,and 0 otherwise,where di denotes the degree of vertex viin G.The matrix generalizes the famous Zagreb matrix(p=1),Sombor matrix (p=2) and inverse sum index matrix (p=-1).In this paper,we find a pair of p-Sombor noncospectral equienergetic graphs and determine some bounds for the p-Sombor(Laplacian) spectral radius.Then we describe the properties of connected graphs with k distinct p-Sombor Laplacian eigenvalues.At last,we determine the Sombor spectrum of some special graphs.As a by-product,we determine the spectral properties of Sombor matrix(p=2),Zagreb matrix(p=1) and inverse sum index matrix(p=-1).

关 键 词：p-Sombor matrix p-Sombor Laplacian matrix p-Sombor spectrum 

分 类 号：O157.5[理学—数学]