On the generalized spectral characterizations of Eulerian graphs (Q668057)

Summary: A graph \(G\) is said to be \textit{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 [J. Comb. Theory, Ser. B 122, 438--451 (2017; Zbl 1350.05098)], \textit{W. Wang} 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.