论文标题
距离频谱半径上的猜想证明和图形的最大传输
A proof of a conjecture on the distance spectral radius and maximum transmission of graphs
论文作者
论文摘要
令$ g $为简单的连接图，而$ d（g）$是$ g $的距离矩阵。假设$ d _ {\ max}（g）$和$λ_1（g）$分别是$ d（g）$的最大行总和和频谱半径。在本文中，我们给出了$ d _ {\ max}（g）-λ_1（g）$的下限，并表征达到界限的极端图。作为推论，我们解决了刘，舒和Xue提出的猜想。
Let $G$ be a simple connected graph, and $D(G)$ be the distance matrix of $G$. Suppose that $D_{\max}(G)$ and $λ_1(G)$ are the maximum row sum and the spectral radius of $D(G)$, respectively. In this paper, we give a lower bound for $D_{\max}(G)-λ_1(G)$, and characterize the extremal graphs attaining the bound. As a corollary, we solve a conjecture posed by Liu, Shu and Xue.
