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Spectra of symmetric powers of graphs and the Weisfeiler–Lehman refinements
2010
Journal of combinatorial theory. Series B (Print)
The k-th power of an 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
doi:10.1016/j.jctb.2010.07.001
fatcat:rjs7iahnbzbhplvkqzgpbb3rt4