给定点连通度的图的补图的无符号拉普拉斯谱半径  

The Signless Laplacian Spectral Radius of the Complements of Graphs with Given Vertex Connectivity

作　　者：李铿 邱欢 张维娟[1] 王国平[1] LI Keng;QIU Huan;ZHANG Wei-juan;WANG Guo-ping(School of Mathematical Sciences,Xinjiang Normal University,Urumqi,Xinjiang,830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《新疆师范大学学报（自然科学版）》2024年第3期64-68,共5页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：新疆维吾尔自治区自然科学基金资助项目(2023D01A38)。

摘　　要：假设G是一个具有点集V(G)={v_(1),v_(2),…,v_(n)}和边集E(G)的连通简单图,矩阵Q(G)=D(G)+A(G)被称为图G的无符号拉普拉斯矩阵,其中D(G)和A(G)分别是图G的度对角矩阵和邻接矩阵。称矩阵Q(G)的最大特征值为图G的无符号拉普拉斯谱半径。图G的补图记为G^(c)=(V(G^(c))),E(G^(c)),这里V(G^(c))=V(G)和E(G^(c))={xy|x,y∈V(G),xy∉E(G)}.文章在给定点连通度且直径大于3的图的所有补图中,确定了无符号拉普拉斯谱半径达到最小时的唯一图。Suppose that G is a connected simple graph with the vertex set V(G)={v_(1),v_(2),…,v_(n)}and the edge set E(G),the matrix Q(G)=D(G)+A(G)is called the signless Laplacian matrix of the graph G,where D(G)and A(G)are the degree diagonal matrix and the adjacency matrix of G,respectively,the maximum eigenvalue of matrix Q(G)is called the signless Laplacian spectral radius of graph G,the complements of G are denoted by G^(c)=(V(G^(c))),E(G^(c)),where V(G^(c))=V(G)and E(G^(c))={xy|x,y∈V(G),xy∉E(G)}.In this paper,we the unique graph is determined that whose signless Laplacian spectral radius is minimum among all complements of graphs with given vertex connectivity and diameter greater than three.

关 键 词：无符号拉普拉斯矩阵 无符号拉普拉斯谱半径 补图 点连通度 

分 类 号：O157.5[理学—数学]