厦门大学学报（自然科学版）2025，Vol.64Issue(6)：1019-1021,3.DOI:10.6043/j.issn.0438-0479.202502013
关于图的特征多项式一些恒等式的初等证明
An elementary proof for some identities related to characteristic polynomials of graphs
摘要
Abstract
[Objective]Herein we study methods of proving identities satisfied by the adjacency polynomials of graphs.[Methods]The definition and properties of the determinant are presented.[Results]Let G=(V,E,ω)be an edge-weighted digraph,andA(G)=(aij)n×nbe its adjacency matrix.Let Φ=(φij(G,x))n×ndenote the adjoint matrix of xIn-A(G).In this note,we give an elementary proof for identities between φij(G,x)and characteristic polynomials of some subgraphs of G.[Conclusions]The proof given in this note is elementary and simple.Moreover,the idea can be used to prove similar identities of other polynomials of graphs.关键词
行列式/伴随矩阵/特征多项式Key words
determinant/adjoint matrix/characteristic polynomial分类
数理科学引用本文复制引用
陈海燕,冯志尧..关于图的特征多项式一些恒等式的初等证明[J].厦门大学学报（自然科学版）,2025,64(6):1019-1021,3.基金项目
国家自然科学基金面上项目(12271210) （12271210）
