{"paper":{"title":"A connection between the bipartite complements of line graphs and the line graphs with two positive eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lee Gumbrell","submitted_at":"2012-04-13T13:11:15Z","abstract_excerpt":"In 1974 Cvetkovi\\'c and Simi\\'c showed which graphs $G$ are the bipartite complements of line graphs. In 2002 Borovi\\'canin showed which line graphs $L(H)$ have third largest eigenvalue $\\lambda_3\\leq0$. Our first observation is that two of the graphs Borovi\\'canin found are the complements of two of the graphs found by Cvetkovi\\'c and Simi\\'c. Using the Courant-Weyl inequalities we show why this is and reprove the result of Borovi\\'canin, highlighting some features of the graphs found by both."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2981","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"}