具有最大Aα-特征值的符号完全图  

On the largest Aα-eigenvalue of signed complete graphs

作　　者：张林 李丹[1] Zhang Lin;Li Dan(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830017

出　　处：《河南师范大学学报（自然科学版）》2024年第4期80-86,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12361071,11901498);新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2021I001).

摘　　要：符号图Σ=(G,σ)由它的底图G=(V,E)与符号函数σ∶E→{-1,1}组成.设α∈[0,1],Belardo定义符号图Aα-矩阵为:A_(α)(Σ)=αD(G)+(1-α)A(Σ),其中A(Σ)是符号图Σ的邻接矩阵,D(G)是G的度对角矩阵.设K n表示n阶完全图,T表示树.设(K_(n),H^(-))表示负边导出子图是H的符号完全图.当0.5<α<1时,确定了符号图(K_(n),T^(-))的最大Aα-特征值达到最大时T的结构.A signed graphΣ=(G,σ)consists of an underlying graph G=(V,E)and a sign functionσ∶E→{-1,1}.LetΣbe a signed graph,the matrix Aα(Σ)is defined by Belardo as follows:A_(α)(Σ)=αD(G)+(1-α)A(Σ),whereα∈[0,1],D(G)is the diagonal matrix of the vertex degrees of G and A(Σ)is the adjacency matrix ofΣ.Let K n denote the complete graph of order n and T be a tree.Let(K_(n),T^(-))be a signed complete graph whose negative edges induce a subgraph H.In this paper,we characterize the extremal signed graph with maximumλ1(A_(α)(Σ))among graphs of type(K_(n),T^(-)).

关 键 词：符号图 完全图 最大特征值 

分 类 号：O175[理学—数学]