{"paper":{"title":"Bounds of Zagreb indices and hyper Zagreb indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jia-Bao Liu, Mohammad R. Farahani, Muhammad K. Jamil, Shaohui Wang, Wei Gao","submitted_at":"2016-12-07T18:39:52Z","abstract_excerpt":"The hyper Zagreb index is a kind of extensions of Zagreb index, used for predicting physicochemical properties of organic compounds. Given a graph $G= (V(G), E(G))$, the first hyper-Zagreb index is the sum of the square of edge degree over edge set $E(G)$ and defined as $HM_1(G)=\\sum_{e=uv\\in E(G)}d(e)^2$, where $d(e)=d(u)+d(v)$ is the edge degree. In this work we define the second hyper-Zagreb index on the adjacent edges as $HM_2(G)=\\sum_{e\\sim f}d(e)d(f)$, where $e\\sim f$ represents the adjacent edges of $G$. By inequalities, we explore some upper and lower bounds of these hyper-Zagreb indic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02361","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"}