图的规范化Laplace和规范化无符号Laplace特征多项式

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (5): 1078-1084.

图的规范化Laplace和规范化无符号Laplace特征多项式

陈丹丹, 马小玲

新疆大学数学与系统科学学院, 乌鲁木齐 830046

收稿日期:2021-12-17 出版日期:2022-09-26 发布日期:2022-09-26
通讯作者: 马小玲 E-mail: mxling2018@163.com

Normalized Laplacian and Normalized Signless Laplacian Characteristic Polynomials of a Graph

CHEN Dandan, MA Xiaoling

College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Received:2021-12-17 Online:2022-09-26 Published:2022-09-26

摘要/Abstract

摘要： 利用行列式的性质, 首先基于图G的Randic矩阵的特征多项式给出规范化Laplace和规范化无符号Laplace特征多项式; 其次, 借助导出子图的特征多项式表示出Randic矩阵以及规范化Laplace和规范化无符号Laplace矩阵的特征多项式; 最后, 给出图G的Middle图的特征多项式.

关键词: 规范化, Laplace特征多项式, 无符号Laplace特征多项式, Randic矩阵

Abstract: Using the properties of determinant, firstly, we gave the normalized Laplacian and normalized signless Laplacian characteristic polynomials based on the characteristic polynomial of the Randic matrix of a graph G. Secondly, we gave the characteristic polynomials of Randic matrix, normalized Laplacian matrix and normalized signless Laplacian matrix by means of the characteristic polynomials of the induced subgraphs. Finally, we gave the characteristic polynomial of the Middle graph of a graph G.

Key words: normalization, Laplacian characteritic polynomial, , signless Laplacian characteristic polynomial, , Randic matrix

中图分类号:

O157.5

陈丹丹, 马小玲. 图的规范化Laplace和规范化无符号Laplace特征多项式[J]. 吉林大学学报(理学版), 2022, 60(5): 1078-1084.

CHEN Dandan, MA Xiaoling. Normalized Laplacian and Normalized Signless Laplacian Characteristic Polynomials of a Graph[J]. Journal of Jilin University Science Edition, 2022, 60(5): 1078-1084.