论文标题
在$ \ {1，-1、0 \} $和最大$ k $ -cut问题的图表上
On graphs with eigenvectors in $\{1, -1, 0\}$ and the max $k$-cut problem
论文作者
论文摘要
在本文中，我们表征了所有图表，其中所有图形都带有无标志性的Laplacian和邻接矩阵，其组件等于$ \ { - 1，0，1 \}。特征值，最小的邻接特征值和图形最大的拉普拉斯特征值。另外，我们为获得的上限构建了极端图的无限家族。
In this paper, we characterize all graphs with eigenvectors of the signless Laplacian and adjacency matrices with components equal to $\{- 1, 0, 1\}.$ We extend the graph parameter max $k$-cut to square matrices and prove a general sharp upper bound, which implies upper bounds on the max $k$-cut of a graph using the smallest signless Laplacian eigenvalue, the smallest adjacency eigenvalue, and the largest Laplacian eigenvalue of the graph. In addition, we construct infinite families of extremal graphs for the obtained upper bounds.
