Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements
| dc.creator | Alzaga, Alfredo | |
| dc.creator | Iglesias, Rodrigo | |
| dc.creator | Pignol, Ricardo | |
| dc.date | 2008-01-15 | |
| dc.date.accessioned | 2026-07-07T08:54:36Z | |
| dc.date.available | 2026-07-07T08:54:36Z | |
| dc.description | 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 well known 2k-dimensional Weisfeiler-Lehman method fails to distinguish two given graphs, then their k-th powers --and their k-th symmetric powers-- are cospectral. As it is well known, there are pairs of non-isomorphic n-vertex graphs which are not distinguished by the k-dim WL method, even for k=Omega(n). In particular, this shows that for each k, there are pairs of non-isomorphic n-vertex graphs with cospectral k-th (symmetric) powers. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0801.2322 | |
| dc.identifier | http://arxiv.org/abs/0801.2322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145991 | |
| dc.subject | Spectral Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 68R10; 05C60 | |
| dc.title | Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements | |
| dc.type | text |