{"paper":{"title":"On extremal trees with respect to the $F$-index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Darko Dimitrov, Hosam Abdo, Ivan Gutman","submitted_at":"2015-09-11T16:14:36Z","abstract_excerpt":"In a study on the structure--dependency of the total $\\pi$-electron energy from 1972, Trinajsti\\'c and one of the present authors have shown that it depends on the sums $\\sum_{v\\in V}d(v)^2$ and $\\sum_{v\\in V}d(v)^3$, where $d(v)$ is the degree of a vertex $v$ of the underling molecular graph $G$. The first sum was later named {\\it first Zagreb index} and over the years became one of the most investigated graph--based molecular structure descriptors. On the other hand, the second sum, except in very few works on the general first Zagreb index and the zeroth--order general Randi\\'c index, has b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03574","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"}