Sharp spectral bounds for the vertex-connectivity of regular graphs

Wenqian Zhang () and Jianfeng Wang ()
Additional contact information
Wenqian Zhang: Shandong University of Technology
Jianfeng Wang: Shandong University of Technology

Journal of Combinatorial Optimization, 2023, vol. 45, issue 2, No 11, 12 pages

Abstract: Abstract Let G be a connected d-regular graph and $$\lambda _2(G)$$ λ 2 ( G ) be the second largest eigenvalue of its adjacency matrix. Mohar and O (private communication) asked a challenging problem: what is the best upper bound for $$\lambda _2(G)$$ λ 2 ( G ) which guarantees that $$\kappa (G) \ge t+1$$ κ ( G ) ≥ t + 1 , where $$1 \le t \le d-1$$ 1 ≤ t ≤ d - 1 and $$\kappa (G)$$ κ ( G ) is the vertex-connectivity of G, which was also mentioned by Cioabă. As a starting point, we determine a sharp bound for $$\lambda _2(G)$$ λ 2 ( G ) to guarantee $$\kappa (G) \ge 2$$ κ ( G ) ≥ 2 (i.e., the case that $$t =1$$ t = 1 in this problem), and characterize all families of extremal graphs.

Keywords: Adjacency matrix; Second largest eigenvalue; Connectivity; Regular graphs; 05C50 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-023-00992-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:45:y:2023:i:2:d:10.1007_s10878-023-00992-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-023-00992-0

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().