一类2n阶图的邻接矩阵的行列式研究  

On the Determinant of Adjacency Matrix of a Family of Graphs of Order 2n

作　　者：霍丽君 冉莎 程卫东 HUO Li-jun;RAN Sha;CHENG Wei-dong(School of Science,Chongqing University of Technology,Chongqing 400054,China;School of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆理工大学理学院,重庆400054 [2]重庆邮电大学理学院,重庆400065

出　　处：《数学的实践与认识》2023年第10期218-226,共9页Mathematics in Practice and Theory

基　　金：重庆市自然科学基金项目(cstc2021jcyj-msxmX0575,CSTB2022NSCQ-MSX0831);重庆邮电大学科研启动基金项目(E011A2019104);重庆理工大学国家自然科学基金培育项目(2022PYZ023);重庆理工大学研究生教育高质量发展行动计划资助成果(gzljg2022319,gzlcx20223306)。

摘　　要：在图论中,图的邻接矩阵是研究图的一个强有力的工具,而其行列式在研究图的结构性质时起到了非常重要的作用,从而受到人们的广泛关注。计算图的邻接矩阵的行列式通常可以采用图论的方法或代数的方法.本文利用线性代数中计算行列式的基本技巧,计算了一类2n阶简单无向图的邻接矩阵的行列式.Adjacency matrix is a powerful tool in the study of graph theory.The determinant of adjacency matrix of a graph plays a very important role in studying the structure properties of the graph,which has attracted extensive attentions.The determinant of adjacency matrix of a graph can usually be calculated by the methods from graph theory or algebra.In this paper,by applications of some basic techniques for computing the determinant in linear algebra,the determinant of the adjacency matrix of a family of simple undirected graphs of order is obtained.

关 键 词：简单无向图 子群包含图 邻接矩阵 行列式 初等变换 

分 类 号：O157.5[理学—数学]