论文标题
三角形阵列中的整体cographs家族
Families of Integral Cographs within a Triangular Arrays
论文作者
论文摘要
\ emph {decterant hosoya triangle}是一个三角形阵列，其中条目是二二个斐波那契矩阵的决定因素。行列式Hosoya三角形$ \ bmod \，2 $产生了三个无限的图表，它们是通过（联合）的两个完整图形的完整产品（JOIN）形成的，这是两个完整的图形，带有空图。我们为这些家族的图表提供了必要和充分的条件。 这些图的某些功能是：它们是整体的cographs，所有图形最多都具有五个不同的特征值，所有图形都是$ d $ rongular graphs，带有$ d = 2,4,6，\ dots $或几乎是规范的图形，其中一些是laplacian积分。最后，我们将其中一些结果扩展到了霍索亚三角。
The \emph{determinant Hosoya triangle}, is a triangular array where the entries are the determinants of two-by-two Fibonacci matrices. The determinant Hosoya triangle $\bmod \,2$ gives rise to three infinite families of graphs, that are formed by complete product (join) of (the union of) two complete graphs with an empty graph. We give a necessary and sufficient condition for a graph from these families to be integral. Some features of these graphs are: they are integral cographs, all graphs have at most five distinct eigenvalues, all graphs are either $d$-regular graphs with $d=2,4,6,\dots $ or almost-regular graphs, and some of them are Laplacian integral. Finally we extend some of these results to the Hosoya triangle.
