论文标题
$ \ MATHCAL {C} $ - 图形的光谱属性
Spectral properties of $\mathcal{C}$-graphs
论文作者
论文摘要
假定是无方向性，简单和连接的是本研究中的所有图形，而邻接矩阵$ a $用作相关矩阵。在本文中，我们表明有可能将创建序列与一种类型的Capchs相关联（我们称其为$ \ Mathcal {C} $ - Graphs）。这些cographs可以通过自然数的有限序列来定义。使用该顺序，我们获得了所考虑的Caph描述的惯性。从$（-1,0）$到$ \ big {[} \ frac {-1- \ sqrt {2}} {2} {2}，-1）\ cup（-1，0）\ cup（0，0， \ frac {-1+ \ sqrt {2}} {2}α_{min} \ big {]} $，（其中$α_{min} \ geq1 $是创建序列的最小整数）。
Assumed to be undirected, simple, and connected are all of the graphs in this study, and adjacency matrix $A$ serves as the associated matrix. In this paper we show that it is possible to relate a creation sequence for a type of cographs (we call it $\mathcal{C}$-graphs). Those cographs can be defined by a finite sequence of natural numbers. Using that sequence we obtain the inertia of the cograph under consideration. An extended eigenvalue-free set from $(-1,0)$ to $\big{[}\frac{-1-\sqrt{2}}{2}, -1)\cup (-1, 0) \cup (0, \frac{-1+\sqrt{2}}{2}α_{min}\big{]}$, (where $α_{min}\geq1$ is the smallest integer of the creation sequence) is obtained for the cographs under consideration. Additionally, an exact formula is found for the characteristic polynomial.
