论文标题
$ q $ - 非双方$ c_ {3} $的最大值 - 免费图
Maxima of the $Q$-index of non-bipartite $C_{3}$-free graphs
论文作者
论文摘要
极端图理论的经典结果（称为Mantel的定理）指出，每个非两部分图$ n $都具有$ $ M> \ lfloor \ frac {n^{2}}} {4} \ rfloor $包含一个三角形。林，宁和吴[梳子。概率。计算。 30（2021）258-270]被证明是Mantel定理的光谱版本，用于给定的订单$n。$ zhai和shu [离散数学。 345（2022）112630]调查了本文的固定尺寸$m。$的光谱版本，我们证明了Mantel定理的$ q $ spectral版本。
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.
