On the Generalized Spectral Characterizations of Eulerian Graphs

Abstract

A graph $G$ is said to be determined by its generalized spectra (DGS for short) if, for any graph $H$, graphs $H$ and $G$ are cospectral with cospectral complements imply that $H$ is isomorphic to $G$. In Wang (J. Combin. Theory, Ser. B, 122 (2017) 438-451), the author gave a simple method for a graph to be DGS. However, the method does not apply to Eulerian graphs. In this paper, we gave a simple method for a large family of Eulerian graphs to be DGS. Numerical experiments are also presented to illustrate the effectiveness of the proposed method.