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

Xinmin Hou, Boyuan Liu, Shicheng Wang +2

Nikiforov (LAA, 2010) conjectured that for given integer $k$, any graph $G$ of sufficiently large order $n$ with spectral radius $\mu (G)\ge \mu (S_{n,k})$ contains all trees of order $…