The generalized 3-connectivity of the Mycielskian of a graph

Shasha Li, Yan Zhao, Fengwei Li and Ruijuan Gu

Applied Mathematics and Computation, 2019, vol. 347, issue C, 882-890

Abstract: The generalized k-connectivity κk(G) of a graph G is a generalization of the concept of the traditional connectivity, which can serve for measuring the capability of a graph G to connect any k vertices in G. In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph μ(G), which is called the Mycielskian of G. In this paper, we investigate the relation between the generalized 3-connectivity of the Mycielskian of a graph G and the generalized 3-connectivity of G, and show that κ3(μ(G))≥κ3(G)+1. Moreover, by this result, we completely determine the generalized 3-connectivity of the Mycielskian of the tree Tn, the complete graph Kn and the complete bipartite graph Ka,b.

Keywords: Generalized 3-connectivity; Mycielskian of a graph; Tree; Complete graph; Complete bipartite graph (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:882-890

DOI: 10.1016/j.amc.2018.11.006

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