In this paper, we confirm that a conjecture on the sum of independence number and average degree of a graph is true, which was posed by Aouchiche, Brinkmann and Hansen (M. Aouchiche, G. Brinkmann and P. Hansen, Variable neighborhood search of extremal graphs. 21. Conjectures and results about the independence number, Discrete Appl. Math.156 (2008) 2530–2542.).
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