论文标题
表征桥的光谱特性
Characterizing Spectral Properties of Bridge
论文作者
论文摘要
桥接图是一种特殊的图形类型，通过将相同的连接图与路径图连接在一起来构建。我们在本文中讨论了不同类型的桥图$ b_ {n \ times l}^{m \ times k} $。特别是，我们讨论以下内容：完整类型的桥图，星形桥图和完整的二进制树桥图。我们还使用光谱图理论中的方法绑定了这些图的图形laplacian的第二个特征值。通常，我们证明，对于一般的桥图，$ b_ {n \ times l}^2 $，图laplacian的第二个特征值应在$ 0 $和$ 2 $之间，包括。最后，我们讨论了在无限桥图上的未来工作。我们创建了定义，并找到了相关定理，以支持我们关于无限桥图的未来工作。
The Bridge graph is a special type of graph which are constructed by connecting identical connected graphs with path graphs. We discuss different types of bridge graphs $B_{n\times l}^{m\times k}$ in this paper. In particular, we discuss the following: complete-type bridge graphs, star-type bridge graphs, and full binary tree bridge graphs. We also bound the second eigenvalues of the graph Laplacian of these graphs using methods from Spectral Graph Theory. In general, we prove that for general bridge graphs, $B_{n\times l}^2$, the second eigenvalue of the graph Laplacian should be between $0$ and $2$, inclusive. In the end, we talk about future work on infinite bridge graphs. We created definitions and found the related theorems to support our future work about infinite bridge graphs.
