EconPapers    
Economics at your fingertips  
 

Path connectivity of line graphs and total graphs of complete bipartite graphs

Wen-Han Zhu, Rong-Xia Hao, Yan-Quan Feng and Jaeun Lee

Applied Mathematics and Computation, 2023, vol. 457, issue C

Abstract: Let θ be a subset of vertex set V(G) of a simply connected graph G, two θ-trees P1 and P2 of G are said to be internally disjoint if V(P1)∩V(P2)=θ and E(P1)∩E(P2)=∅. For an integer k≥2, the k-path connectivity πk(G) (resp. k-tree connectivity κk(G)) of a graph G is defined as min{πG(θ)|θ⊆V(G)and|θ|=k} (resp. min{κG(θ)|θ⊆V(G)and|θ|=k}), where πG(θ) (resp. κG(θ)) is the maximum number of pairwise internally disjoint θ-paths (resp. θ-trees) in G. The 3-tree connectivity of the line graph L(Km,n) and total graph T(Km,n) of the complete bipartite graph Km,n are gotten in [Appl. Math. Comput. 347(2019) 645-652]. In this paper, these results are improved from trees to paths. The exact values of the 3-path connectivity for L(Km,n) and T(Km,n) are gotten. That is, π3(L(Km,n))=⌊3m+2n−34⌋−1 for m=3 and odd n, otherwise, π3(L(Km,n))=⌊3m+2n−34⌋ unless m=1 and n=1,2; π3(T(Km,n))=m+⌊m4⌋ for n≥m≥1. In addition, the compact upper bound of π3(G) for a general graph G are gotten.

Keywords: k-path connectivity; internally disjoint S-paths; line graph; total graph (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032300351X
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:457:y:2023:i:c:s009630032300351x

DOI: 10.1016/j.amc.2023.128182

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 ().

 
Page updated 2025-03-19
Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s009630032300351x