{"paper":{"title":"A note on polyomino chains with extremum general sum-connectivity index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akbar Ali, Tahir Idrees","submitted_at":"2018-03-13T07:02:03Z","abstract_excerpt":"The general sum-connectivity index of a graph $G$ is defined as $\\chi_{\\alpha}(G)= \\sum_{uv\\in E(G)} (d_u + d_{v})^{\\alpha}$ where $d_{u}$ is degree of the vertex $u\\in V(G)$, $\\alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $\\chi_{\\alpha}$ values from a certain collection of polyomino chain graphs is solved for $\\alpha<0$. The obtained results together with already known results (concerning extremum values of polyomino chain graphs) give the complete solution of the aforement"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04657","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"}