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Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements
[article]
2008
arXiv
pre-print
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
arXiv:0801.2322v1
fatcat:pipljprlabch7aazvj3r6ai6uq