图的Sum-connectivity指标与其无符号拉普拉斯谱半径  

Sum-connectivity index of a graph and its signless laplacian spectral radius

作　　者：王月卿 林雅津 WANG Yue-qing;LIN Ya-jin(School of Computer,Minnan Normal University,Zhangzhou 363000,China;School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学计算机学院,福建漳州363000 [2]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《青海师范大学学报（自然科学版）》2023年第4期63-67,共5页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：福建省中青年教师教育科研项目(JAT200330)

摘　　要：设G=(V,E)为简单连通图.图G的Sum-connectivity指标被定义为χ(G)=Σuv∈E(G)2/√d_(u)+d_(v),其中d_(u)表示顶点u的度.用q(G)表示图G的无符号拉普拉斯谱半径.本文研究了χ(G)与q(G)之间的关系,证明了对于所有顶点数n≥3的简单连通图G,都有q(G)/χ^(2)(G)≤n^(2)/(n-1)^(2)等式成立当且仅当G■S_(n).Let G=(V,E)be a simple connected graph.The Sum-connectivity index of G is defined asχ(G)=Σuv∈E(G)2/√d_(u)+d_(v),where d_(u)is the degree of the vertex u.Let q(G)be the signless Laplacian spectral radius of G.We study the relationship betweenχ(G)and q(G)and prove that for any connected graph G of order n≥3,q(G)/χ^(2)(G)≤n^(2)/(n-1)^(2),with equality if and only if G■S_(n).

关 键 词：Sum-connectivity指标 无符号拉普拉斯矩阵 特征值 

分 类 号：O157.5[理学—数学]