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arXiv · 1610.00833

The spectral radius of graphs without trees of diameter at most four

Xinmin Hou·Boyuan Liu·Shicheng Wang·Jun Gao·Chenhui Lv
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Abstract

Nikiforov (LAA, 2010) conjectured that for given integer $k$, any graph $G$ of sufficiently large order $n$ with spectral radius $μ(G)\geq μ(S_{n,k})$ contains all trees of order $2k+2$, unless $G=S_{n,k}$, where $S_{n,k}=K_k\vee \overline{K_{n-k}}$, the join of a complete graph of order $k$ and an empty graph of order $n-k$. In this paper, we show that the conjecture is true for trees of diameter at most four.

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Xinmin Hou, Boyuan Liu, Shicheng Wang, Jun Gao, Chenhui Lv. 2018-08-02. The spectral radius of graphs without trees of diameter at most four. https://arxiv.org/abs/1610.00833

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