Triangle-free Graphs with Three Positive Eigenvalues  

作　　者：Fang Duan 

机构地区：[1]School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China

出　　处：《Algebra Colloquium》2024年第3期525-540,共16页代数集刊（英文版）

基　　金：Supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(No.2022D01A218);the Doctoral Scientific Research Foundation of Xinjiang Normal University(No.XJNUBS2009).

摘　　要：A graph G is called triangle-free if G does not contain any triangle as its induced subgraph.Let G_(n)be the set of triangle-free graphs of order n each of which has three positive eigenvalues.In this paper,we find 20 specific graphs in G_(n),each of which has nullity no more than 2,and we show that in terms of three graph transformations all the other graphs of G_(n)can be constructed from these 20 specific graphs.Hence,we completely characterize the triangle-free graphs with exactly three positive eigenvalues.

关 键 词：positive(negative)inertia index NULLITY triangle-free graph 

分 类 号：O157.5[理学—数学]