{"paper":{"title":"On the Extremal Graphs with Respect to Bond Incident Degree Indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akbar Ali, Darko Dimitrov","submitted_at":"2017-07-03T19:17:22Z","abstract_excerpt":"Many existing degree based topological indices can be classified as bond incident degree (BID) indices, whose general form is $BID(G)=\\sum_{uv\\in E(G)}$ $\\Psi(d_{u},d_{v})$, where $uv$ is the edge connecting the vertices $u,v$ of the graph $G$, $E(G)$ is the edge set of $G$, $d_{u}$ is the degree of the vertex $u$ and $\\Psi$ is a non-negative real valued (symmetric) function of $d_{u}$ and $d_{v}$. Here, it has been proven that if the extension of $\\Psi$ to the interval $[0,\\infty)$ satisfies certain conditions then the extremal $(n,m)$-graph with respect to the BID index (corresponding to $\\P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00733","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"}