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Research Article | Open Access

Generalized (edge-)connectivity of join, corona and cluster graphs

Meiqin Wei1, He Zhang2, Zhao Wang3( ), Yaping Mao4
College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China
Department of Mathematics, Qinghai Normal University, Xining, Qinghai 810008, China
College of Science, China Jiliang University, Hangzhou, Zhejiang 310018, China
Academy of Plateau Science and Sustainability, Qinghai Normal University, Xining, Qinghai 810008, China

*In Summer 2020, this paper was accepted for publication in "Ars Combinatoria". As of Dec 15, 2021, the editorial board and managing editors of this journal have resigned. So we contacted the publisher and withdrawn the paper from "Ars Combinatoria" and re-submitted here.

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Abstract

The generalized k-connectivity κ k ( G ) of a graph G, introduced by Hager in 1985, is a natural generalization of the classical connectivity. As a natural counterpart, Li et al. proposed the concept of generalized k-edge-connectivity λ k ( G ). In this paper, we obtain exact values or sharp upper and lower bounds of κ k ( G ) and λ k ( G ) for join, corona and cluster graphs.

Keywords

Steiner treegeneralized connectivityjoincoronacluster
CLC number: 05C40, 05C05, 05C76

References

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16775-16786
DOI: 10.3934/math.2022921

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Cite this article:
Wei M, Zhang H, Wang Z, et al. Generalized (edge-)connectivity of join, corona and cluster graphs. AIMS Mathematics, 2022, 7(9): 16775-16786. https://doi.org/10.3934/math.2022921

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Received: 25 April 2022
Revised: 26 June 2022
Accepted: 07 July 2022
Published: 15 September 2022
©2022 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)