论文标题
Ramanujan图的图形刚度特性
Graph rigidity properties of Ramanujan graphs
论文作者
论文摘要
Cioabă，Dewar和Gu的最新结果暗示，任何$ k $ ramanujan图形都带有$ k \ geq 8 $，均以$ \ mathbb {r}^2 $全球固定。在本文中，我们扩展了这些结果，并证明任何$ k $ ramanujan的图形都足够大，在$ \ mathbb {r}^2 $中都固定在\ in \ {6，7 \} $中，以及当$ k \ in \ in \ in \ in \ in \ in \ in \ {4,5 \} $也是vertex-nimansive vertexx-transive。这些结果表明，由Morgenstern在1994年构建的Ramanujan图是全球刚性的。我们还证明了其他类型的框架刚性的结果，包括革命表面上的刚性刚度，螺距刚度和刚性。此外，我们使用计算方法来确定哪些小订单的ramanujan图在$ \ mathbb {r}^2 $中都固定在全球范围内。
A recent result of Cioabă, Dewar and Gu implies that any $k$-regular Ramanujan graph with $k\geq 8$ is globally rigid in $\mathbb{R}^2$. In this paper, we extend these results and prove that any $k$-regular Ramanujan graph of sufficiently large order is globally rigid in $\mathbb{R}^2$ when $k\in \{6, 7\}$, and when $k\in \{4,5\}$ if it is also vertex-transitive. These results imply that the Ramanujan graphs constructed by Morgenstern in 1994 are globally rigid. We also prove several results on other types of framework rigidity, including body-bar rigidity, body-hinge rigidity, and rigidity on surfaces of revolution. In addition, we use computational methods to determine which Ramanujan graphs of small order are globally rigid in $\mathbb{R}^2$.
