Two relations between the parameters of independence and irredundance

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Abstract

In a simple graph, n, δ, i and IR denote respectively the number of vertices, the minimum degree, the order of a minimum maximal independent set and the order of a maximum irredundant set. We show that i + IR⩽2n + 2δ − 22nδ, which was conjectured by Cockayne, Favaron, Payan and Thomason, and that i + 2δIR⩽n + δ.

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