AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (837.2 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Laplacian controllability analysis of chain graph based on minimal perfect critical vertex set

College of Science, National University of Defense Technology, Changsha 410073, Hunan, China
Show Author Information

Abstract

The aim is to find all of the minimum leader set for chain graphs. By analyzing the subgraph structure rather than the eigenvectors, minimal perfect critical vertex sets (MPCS) of chain graph are found. It is proved that there is one and only one MPCS in chain graph (CG) (1, 1, ⋯, 1; 1, 1, ⋯, 1), and it is a 4-MPCS. Based on this, all the minimum leader sets of the chain graph are given.

Keywords

minimal perfect critical vertex setchain graphLaplacian controllabilityminimum leader setsubgraph structure
CLC number: 05C50, 15A18, 93A16

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 11 Issue 3,
March 2026
Pages 7766-7778
DOI: 10.3934/math.2026319

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Dai L. Laplacian controllability analysis of chain graph based on minimal perfect critical vertex set. AIMS Mathematics, 2026, 11(3): 7766-7778. https://doi.org/10.3934/math.2026319

0

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 23 November 2025
Revised: 02 March 2026
Accepted: 05 March 2026
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)