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Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 154940 Total View: 1848051
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2023.12.007

The Generalized 4-Edge Connectivity of Line Graphs of the Complete Bipartite Graph

Liqun Wei*, Yinkui Li

Department of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai, China.

*Corresponding author: Liqun Wei

Published: January 24,2024

Abstract

Connectivity is one of the most basic concepts of graph-theoretical subjects, both in a combinatorial sense and in an algorithmic sense. The generalized k-edge connectivity of G is a natural generalization of the traditional edge connectivity and defined as λk (G)=min{λ(S)| S⊆V(G),|S|=k}, where λ(S) is the maximum number of internally edge disjoint Steiner trees connecting S in G. In 2022, Zhao and Hao determined the generalized 4-connectivity of line graphs of the complete bipartite graph in Applied Mathematics and Computation. In this paper, we determined the generalized 4-edge connectivity of the line graph of the complete bipartite graph and showed that λk (G)=m+n-3.

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How to cite this paper

The Generalized 4-Edge Connectivity of Line Graphs of the Complete Bipartite Graph

How to cite this paper: Liqun Wei, Yinkui Li. (2023) The Generalized 4-Edge Connectivity of Line Graphs of the Complete Bipartite GraphJournal of Applied Mathematics and Computation7(4), 478-482.

DOI: http://dx.doi.org/10.26855/jamc.2023.12.007