Minimum Distance Spectral Radius of Tree with Given Maximum Degree

Source abstract

In this article, the unique graph with minimum distance spectral radius among trees with given order $n$ and maximum degree $\varDelta$ is determined, where $2\varDelta+1 \leq n \leq \varDelta^{2} +1$ for $\varDelta \geq 3$. This article is a part proof of the conjecture proposed in $\cite{ref1}$.