联并图的广义谱  

Universal spectra of some joined union graphs

作　　者：王洪波[1] WANG Hong-bo(School of Sciences,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《青海师范大学学报（自然科学版）》2022年第2期4-9,共6页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：福建省自然科学基金(2021J01860);福建省教育厅中青年教师教育科研项目(JAT190325)

摘　　要：广义邻接矩阵U(G)=αA(G)+βI+γJ+δD(G)是图谱理论中许多常研究矩阵的推广,这里α(≠0),β,γ,δ是实数,A(G),D(G),I,J分别表示图G的邻接矩阵,度矩阵,单位矩阵和全1矩阵.本文利用矩阵的性质刻划了联并图的广义谱和特征多项式.利用以上刻划给出了一个构造参数为(α,β,γ,0)的等广义能量图的方法.The universal adjacency matrix U(G)=αA(G)+βI+γJ+δD(G)of a graph,in whichα(≠0),β,γ,δare real numbers,A(G),D(G),I,J are the adjacency matrix of G,degree matrix of G,unit matrix and all 1’s matrix respectively,is the generalization of many matrices often studied in the graph spectrum theory.In this paper by matrix theory we give the characterization of the universal spectra and characteristic polynomials of some joined union graphs.By this characterization a method of constructing universal equienergetic graphs with Parameters(α,β,γ,0)is given.

关 键 词：广义邻接矩阵 广义谱 特征多项式 等广义能量图 

分 类 号：O157.5[理学—数学]