Regular and Maximal Graphs with Prescribed Tripartite Graph as a Star Complement  

作　　者：Xiaona FANG Lihua YOU 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第4期517-532,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11971180,12271337);the Guangdong Provincial Natural Science Foundation(No.2019A1515012052)。

摘　　要：Let G be a graph of order n andμbe an adjacency eigenvalue of G with multiplicity k≥1.A star complement H forμin G is an induced subgraph of G of order n-k with no eigenvalueμ,and the subset X=V(G-H)is called a star set forμin G.The star complement provides a strong link between graph structure and linear algebra.In this paper,the authors characterize the regular graphs with K2,2,s(s≥2)as a star complement for all possible eigenvalues,the maximal graphs with K2,2,s as a star complement for the eigenvalueμ=1,and propose some questions for further research.

关 键 词：Adjacency eigenvalue Star set Star complement Regular graph Maximal graph 

分 类 号：O157.5[理学—数学]