Annihilating polynomial, Jordan canonical from, and generalized spectral characterizations of Eulerian graphs

Kunyue Li, Wei Wang, Hao Zhang

Let $G$ be an Eulerian graph on $n$ vertices with adjacency matrix $A$ and characteristic polynomial $\varphi (x)$. We show that when $n$ is even (resp. odd), the square-root of $\varphi (x)$ (r…