{"paper":{"title":"Signed graphs cospectral with the path","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hamid Reza Maimani, Leila Parsaei Majd, Saieed Akbari, Willem H. Haemers","submitted_at":"2017-09-28T08:52:31Z","abstract_excerpt":"A signed graph $\\Gamma$ is said to be determined by its spectrum if every signed graph with the same spectrum as $\\Gamma$ is switching isomorphic with $\\Gamma$. Here it is proved that the path $P_n$, interpreted as a signed graph, is determined by its spectrum if and only if $n\\equiv 0, 1$, or 2 (mod 4), unless $n\\in\\{8, 13, 14, 17, 29\\}$, or $n=3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09853","kind":"arxiv","version":2},"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"}