Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements

@article{Alzaga2010SpectraOS,
title={Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements},
author={Afredo Alzaga and Rodrigo Iglesias and Ricardo Pignol},
journal={J. Comb. Theory, Ser. B},
year={2010},
volume={100},
pages={671-682}
}

The k-th power of a n-vertex graph X is the iterated cartesian product of X with itself. The k-th symmetric power of X is the quotient graph of certain subgraph of its k-th power by the natural action of the symmetric group. It is natural to ask if the spectrum of the k-th power –or the spectrum of the k-th symmetric power– is a complete graph invariant for small values of k, for example, for k = O(1) or k = O(log n). In this paper, we answer this question in the negative: we prove that if the… CONTINUE READING