Note for the conjecture on the generalized 4-connectivity of total graphs of the complete bipartite graph

Yinkui Li and Liqun Wei

Applied Mathematics and Computation, 2023, vol. 458, issue C

Abstract: The generalized k-connectivity κk(G) of a graph G, introduced by Hager in 1985, is a natural generalization of the concept of connectivity κ(G), which is just for k=2. Rongxia Hao et al. determined the generalized 4-connectivity of the total graphs of the complete equipartition bipartite graph and conjectured that κ4(T(Km,m+1))=2m−1 and κ4(T(Km,n))=2m for n>m+1 and m≥4 in [Appl. Math. Comput. 422 (2022)]. In this paper, we solved this conjecture.

Keywords: The generalized 4-connectivity; Line graph; Total graph; Complete bipartite graph (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300323003946
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:458:y:2023:i:c:s0096300323003946

DOI: 10.1016/j.amc.2023.128225

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().