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[1]李晓琳,王洪波,陈海燕.完全分裂图的临界理想[J].集美大学学报(自然科学版),2022,27(4):359-364.
　LI Xiaolin,WANG Hongbo,CHEN Haiyan.Critical Ideals of the Complete Split Graph[J].Journal of Jimei University,2022,27(4):359-364.
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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

卷:
第27卷
期数:
2022年第4期
页码:
359-364
栏目:
数理科学与信息工程
出版日期:
2022-07-28

文章信息/Info

Title:
Critical Ideals of the Complete Split Graph
作者:
李晓琳; 王洪波; 陈海燕
(集美大学理学院,福建 厦门 361021)
Author(s):
LI Xiaolin; WANG Hongbo; CHEN Haiyan
(School of Science,Jimei University,Xiamen 361021,China)
关键词:
广义拉普拉斯矩阵; 完全分裂图; 临界理想; 临界群
Keywords:
generalized Laplacian matrix; complete split graph; critical ideal; critical group
分类号:
-
DOI:
-
文献标志码:
A
摘要:
一个图G的k阶临界理想是由它的广义拉普拉斯矩阵的所有k阶子式生成的理想，可被看作是图G的邻接特征多项式和拉普拉斯特征多项式的推广。临界理想与图的许多指标密切相关。利用线性代数的方法，得到完全分裂图的临界理想的具体表达式，然后利用此表达式完全确定其临界群的结构。
Abstract:
The k order critical ideal of a graph G is an ideal generated by all minors of size k of its generalized Laplacian matrix,which is considered as the generalization of the characteristic polynomials of its adjacency matrix and Laplacian matrix.The critical ideal was closely connected to many graph indices.In this paper,explicit expressions for critical ideals of a complete split graph were obtained by using linear algebra method.Furthermore,based on these expressions,the structure of the critical group of the complete split graph was determined.

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更新日期/Last Update: 2022-09-10