论文标题
Hadamard对角线可划分的秩序最多36
Hadamard diagonalizable graphs of order at most 36
论文作者
论文摘要
如果图形的拉普拉斯矩阵具有带有条目$ \ pm1 $的完整的正交特征向量，则随着列形成的矩阵作为特征向量是hadamard矩阵而形成的矩阵，并且该图是hadamard diagogonalizalizables。 在本文中，我们证明，如果$ n = 8k+4 $唯一可能的hadamard可对角度图是$ k_n $，$ k_ {n/2，n/2} $，$ 2K_ {n/2} $和$ nk_1 $，并且我们开发了一个有效的计算，以确定所有图形diagonalal a diagonalal a dia dia dia dia dia dia dia dia dia a dia dia aftrix。使用这两种工具，我们确定并呈现所有Hadamard对角度图，直到订单36。
If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries $\pm1$, then the matrix formed by taking the columns as the eigenvectors is a Hadamard matrix and the graph is said to be Hadamard diagonalizable. In this article, we prove that if $n=8k+4$ the only possible Hadamard diagonalizable graphs are $K_n$, $K_{n/2,n/2}$, $2K_{n/2}$, and $nK_1$, and we develop an efficient computation for determining all graphs diagonalized by a given Hadamard matrix of any order. Using these two tools, we determine and present all Hadamard diagonalizable graphs up to order 36. Note that it is not even known how many Hadamard matrices there are of order 36.
