论文标题
具有给定支配数的图的最小光谱半径
The minimum spectral radius of graphs with a given domination number
论文作者
论文摘要
令$ \ mathbb {g} _ {n，γ} $为$ n $顶点上的简单和连接的图表，并具有统治数量$γ$。 $ \ mathbb {g} _ {n，γ} $之间具有最小光谱半径的图为最小化图。在本文中，我们首先证明了$ \ mathbb {g} _ {n，γ} $的最小化图必须是一棵树。此外，对于$γ\ in \ {1,2,3，\ lceil \ frac {n} {n} {3} \ rceil，\ lfloor \ frac {n} {n} {2} \ rfloor \} $
Let $\mathbb{G}_{n,γ}$ be the set of simple and connected graphs on $n$ vertices and with domination number $γ$. The graph with minimum spectral radius among $\mathbb{G}_{n,γ}$ is called the minimizer graph. In this paper, we first prove that the minimizer graph of $\mathbb{G}_{n,γ}$ must be a tree. Moreover, for $γ\in\{1,2,3,\lceil\frac{n}{3}\rceil,\lfloor\frac{n}{2}\rfloor\}$, we characterize all minimizer graphs in $\mathbb{G}_{n,γ}$.
