链图的距离特征值  

The distance spectra of chain graphs

作　　者：吕雪征 马梦郁 LYU Xuezheng;MA Mengyu(School of Mathematics,Renmin University of China,Beijing 100872,China)

机构地区：[1]中国人民大学数学学院,北京100872

出　　处：《运筹学学报（中英文）》2024年第1期112-120,共9页Operations Research Transactions

基　　金：国家自然科学基金(No.11971479)。

摘　　要：如果一个图G不包含2K_(2),C_(3)及C_(5)作为导出子图,称其为链图。在所有点数和边数给定的连通二部图中,链图具有最大的谱半径,这使得链图在图谱理论中占有一席之地。本文研究了连通链图距离特征值的分布情况。对于点数为n的连通链图G=G(t_(1),…,t_(h);s_(1),…,s_(h)),我们证明了-2是G的重数为n-2h的距离特征值,且G有h-1个距离特征值小于-2和h+1个距离特征值大于-2。A graph is called a chain graph if it does not contain induced 2K_(2),C_(3) or C_(5).In spectral graph theory,chain graphs feature as graphs whose largest eigenvalue within the connected bipartite graphs of fixed order and size is maximal.In this paper,we consider the distance eigenvalues of a connected chain graph G.We present that-2 is an eigenvalue of G=G(t_(1),…,t_(h);s_(1),…,s_(h)),with multiplicity n-2h.And further more,there are exactly h-1 eigenvalues less than-2 and exactly h+1 eigenvalues greater than-2.

关 键 词：链图 距离特征值 合理划分 

分 类 号：O221.2[理学—运筹学与控制论]