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Connectivity of the Generalised Mycielskian of Digraphs

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Abstract

In a search for triangle-free graphs with arbitrarily large chromatic number, Mycielski developed a graph transformation that transforms a graph G into a new graph μ(G), which is called the Mycielskian of G. A generalisation of this transformation is the generalised Mycielskian μ m (G), m a positive integer. This paper investigates the vertex-connectivity κ and arc-connectivity κ′ of the generalised Mycielskian of strongly connected digraphs D. We show that κ (μ m (D)) = min{δ(μ m (D)), (m + 1)κ (D) + 1} and κ′ (μ m (D)) = δ(μ m (D)) where δ(μ m (D)) denotes the minimum degree of the generalised Mycielisian μ m (D). This turns out to be a generalisation of the results due to Guo and Guo (Appl. Math. Lett. 22:1622–1625, 2009).

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Author notes

  1. S. Francis Raj

    Present address: Department of Mathematics, Pondicherry University, Puducherry, 605014, India

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  1. Department of Mathematics, Bharathidasan University, Tiruchirappalli, 620024, India

    S. Francis Raj

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  1. S. Francis Raj
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Correspondence to S. Francis Raj.

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Francis Raj, S. Connectivity of the Generalised Mycielskian of Digraphs. Graphs and Combinatorics 29, 893–900 (2013). https://doi.org/10.1007/s00373-012-1151-5

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  • DOI: https://doi.org/10.1007/s00373-012-1151-5

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