论文标题
非双方图的最大光谱半径禁止短奇数循环
The maximum spectral radius of non-bipartite graphs forbidding short odd cycles
论文作者
论文摘要
众所周知，图的特征值可用于描述图的结构属性和参数。 Nosal的定理指出，如果$ g $是带有$ m $边缘的三角形图，则$λ（g）\ le \ sqrt {m} $，当且仅当$ g $是完整的两部分图形时，equality才能保持。最近，Lin，Ning和Wu [Combin。概率。计算。 30（2021）]被证明是非双方三角形图的概括。此外，Zhai和Shu [离散数学。 345（2022）]提出了进一步的改进。在本文中，我们提出了一种证明Zhai和Shu改进的替代方法。此外，该方法可以使我们能够对Zhai和Shu的结果进行改进，以供无奇数循环的非两部分图。
It is well-known that eigenvalues of graphs can be used to describe structural properties and parameters of graphs. A theorem of Nosal states that if $G$ is a triangle-free graph with $m$ edges, then $λ(G)\le \sqrt{m}$, equality holds if and only if $G$ is a complete bipartite graph. Recently, Lin, Ning and Wu [Combin. Probab. Comput. 30 (2021)] proved a generalization for non-bipartite triangle-free graphs. Moreover, Zhai and Shu [Discrete Math. 345 (2022)] presented a further improvement. In this paper, we present an alternative method for proving the improvement by Zhai and Shu. Furthermore, the method can allow us to give a refinement on the result of Zhai and Shu for non-bipartite graphs without short odd cycles.
