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Maxima of the $Q$-index of non-bipartite $C_{3}$-free graphs (2209.00801v1)
Published 2 Sep 2022 in math.CO
Abstract: A classic result in extremal graph theory, known as Mantel's theorem, states that every non-bipartite graph of order $n$ with size $m>\lfloor \frac{n{2}}{4}\rfloor$ contains a triangle. Lin, Ning and Wu [Comb. Probab. Comput. 30 (2021) 258-270] proved a spectral version of Mantel's theorem for given order $n.$ Zhai and Shu [Discrete Math. 345 (2022) 112630] investigated a spectral version for fixed size $m.$ In this paper, we prove $Q$-spectral versions of Mantel's theorem.