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arXiv · 2204.09884

The maximum spectral radius of non-bipartite graphs forbidding short odd cycles

Yongtao Li·Yuejian Peng
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Abstract

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.

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Yongtao Li, Yuejian Peng. 2022-04-26. The maximum spectral radius of non-bipartite graphs forbidding short odd cycles. https://doi.org/10.37236/11236

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