三次图的谱的间隙集
Gap Sets for the Spectra of Cubic Graphs
摘要：
本文研究了大的有限三次图的邻接矩阵的谱中的空隙。已知在三次Ramanujan图和线图中获得的间隙间隔$(2 \sqrt{2},3)$和$[-3,-2)$是最大的。我们给出了[-3，3]中最大间隙的谱的约束，并构造了实现这些边界的例子。这些图产生最大间隙间隔的新实例。我们还证明了$[-3,3)$中的每一个点都可以被三次图，甚至是平面图所缺。我们的结果表明，三次图，甚至平面三次图的谱的研究是微妙的，非常丰富。
英文摘要：
We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals $(2 \sqrt{2},3)$ and $[-3,-2)$ achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [-3,3] which are maximally gapped and construct examples which achieve these bounds. These graphs yield new instances of maximally gapped intervals. We also show that every point in $[-3,3)$ can be gapped by cubic graphs, even by planar ones. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
