Circulant matrices and the spectrum of de Bruijn graphs - Strok, V.V. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
The block structure of $k$-circulant matrices $A$ of order $n(k≥ 2, k| n)$ is investigated and statements, enabling to reduce a series of problems with the matrices $A+A^T$ to analogous problems with matrices of lower order, namely the blocks of the matrices $A$ and $A^T$, are proved. The spectrum and the number of spanning trees of an undirected de Bruijn graph are obtained.