{"paper":{"title":"A simple arithmetic criterion for graphs being determined by their generalized spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wei Wang","submitted_at":"2014-10-08T15:28:09Z","abstract_excerpt":"A graph $G$ is said to be determined by its generalized spectrum (DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with cospectral complements implies that $H$ is isomorphic to $G$.\n  It turns out that whether a graph $G$ is DGS is closely related to the arithmetic properties of its walk-matrix. More precisely, let $A$ be the adjacency matrix of a graph $G$, and let $W =[e, Ae, A^2e,...,A^{n-1}e]$ ($e$ is the all-one vector) be its \\textit{walk-matrix}. Denote by $\\mathcal{G}_n$ the set of all graphs on $n$ vertices with $\\det(W)\\neq 0$. In [Wang, Generalized spectral characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2164","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}