关于任意提升图的泛邻接矩阵的谱与特征空间的注记
A note on the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
摘要：
图$Γ$的泛邻接矩阵$U$，具有邻接矩阵$A$，是$A$、顶点度的对角矩阵$D$、单位矩阵$I$和实系数全1矩阵$J$的线性组合，即$U=c_1 A+c_2 D+c_3 I+ c_4 J$，具有$c_i\in {\mathbb R}$和$c_1\neq 0$。因此，作为特定情况，$U$可以是邻接矩阵、拉普拉斯算子、无符号拉普拉斯算子和赛德尔矩阵。在本文中，我们证明了作者以前介绍的基本上相同的方法可以用于确定任意提升图（正则或非正则）的所有相应特征空间的谱和基。
英文摘要：
The universal adjacency matrix $U$ of a graph $Γ$, with adjacency matrix $A$, is a linear combination of $A$, the diagonal matrix $D$ of vertex degrees, the identity matrix $I$, and the all-1 matrix $J$ with real coefficients, that is, $U=c_1 A+c_2 D+c_3 I+ c_4 J$, with $c_i\in {\mathbb R}$ and $c_1\neq 0$. Thus, as particular cases, $U$ may be the adjacency matrix, the Laplacian, the signless Laplacian, and the Seidel matrix. In this note, we show that basically the same method introduced before by the authors can be applied for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
