An excluding algorithm for testing whether a family of graphs are determined by their generalized spectra

What kinds of graphs are determined by their spectra (DS for short) is a difficult problem in spectral graph theory. In [W. Wang, C.X. Xu, A sufficient condition for a family of graphs being determined by their generalized spectra, European J. Combin., in press], the authors give a sufficient condition for a family of graphs being DS with respect to their generalized spectra. However, there are many graphs in this family, which do not satisfy the condition. To investigate the DS property of graphs in such a situation, an excluding algorithm is presented in this paper, which is proved to be simple and effective as illustrated by some numerical examples.