{"paper":{"title":"Laplacian Spectral Determination of Path-Friendship Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.R. Ashrafi, A.Z. Abdian, L.W. Beineke, M.R. Oboudi","submitted_at":"2019-03-26T19:16:06Z","abstract_excerpt":"A graph $G$ is said to be determined by the spectrum of its Laplacian matrix (DLS) if every graph with the same spectrum is isomorphic to $G$. van Dam and Haemers (2003) conjectured that almost all graphs have this property, but that is known to be the case only for a very few families. In some recent papers it is proved that the friendship graphs and starlike trees are DLS. If a friendship graph and a starlike tree are joined by merging their vertices of degree greater than 2, then the resulting graph is called a path-friendship graph. In this paper, it is proved that the path-friendship grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11121","kind":"arxiv","version":1},"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"}