Trees with Prescribed Maximum Degree and Spectral Radius

Fengming Dong, Ruixue Zhang

It is well known that the spectral radius $\rho (T)$ of a tree $T$ with at least $3$ vertices satisfies $\frac{1}{4}\rho (T{)}^2+1<\Delta (T)\le \rho (T{)}^2$, where $\Delta (T)$ is the maximum degree of $T$. Le…