负惯性指数为2的图的结构刻画  

Complete characterization of graphs with exactly two negative eigenvalues

作　　者：王爽[1] 段芳[1] WANG Shuang;DUAN Fang(School of Mathematics Science,Xinjiang Normal University,Urumqi 830017,Xinjiang,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：《山东大学学报（理学版）》2023年第11期160-164,共5页Journal of Shandong University(Natural Science)

基　　金：新疆维吾尔自治区自然科学基金资助项目(2022D01A218);新疆师范大学基金资助项目(SDJG2021-01)。

摘　　要：用符号Γ_(n)表示点数为n、负惯性指数为2的所有图构成的图集。利用定义的图的3种合同变换,在图集Γ_(n)中可以找出8个零度不超过2的特殊的图,使得图集Γ_(n)中其它图都可以由这8个特殊的图构造出来。因此,负惯性指数为2的图得到了完整的刻画。LetΓ_(n) be the set of graphs of order n such that each of them has exactly two negative eigenvalues.In this paper,we introduce 3 graph transformations.Furthermore,we find 8 specific graphs inΓ_(n),each of them has nullity no more than two and we show that,in terms of the above three congruent transformations of graph,all the other graphs ofΓ_(n) can be constructed from these 8 specific graphs.Hence we completely characterize the graphs with exactly two negative eigenvalues.

关 键 词：负惯性指数 正惯性指数 零度 合同变换 

分 类 号：O157.5[理学—数学]