论文标题
用于立方图的光谱的间隙集
Gap Sets for the Spectra of Cubic Graphs
论文作者
论文摘要
我们研究了大有限立方图的邻接矩阵光谱中的差距。众所周知，差距间隔$（2 \ sqrt {2}，3）$和$ [ - 3，-2）$在Cubic Ramanujan图中获得的$和线图是最大的。我们在[-3,3]中对光谱的限制给出了最大程度的间隙并构建实现这些界限的示例。这些图产生了最大间隔间隔的新实例。我们还表明，即使是平面图，也可以通过$ [-3,3）$中的每个点来掩盖。我们的结果表明，对立方体甚至平面立方的光谱研究的研究非常微妙而非常丰富。
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.
