{"paper":{"title":"On the Zagreb Indices Equality","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":"2011-06-09T13:43:40Z","abstract_excerpt":"For a simple graph $G$ with $n$ vertices and $m$ edges, the first Zagreb index and the second Zagreb index are defined as $M_1(G)=\\sum_{v\\in V}d(v)^2 $ and $M_2(G)=\\sum_{uv\\in E}d(u)d(v)$. In \\cite{VGFAD}, it was shown that if a connected graph $G$ has maximal degree 4, then $G$ satisfies $M_1(G)/n = M_2(G)/m$ (also known as the Zagreb indices equality) if and only if $G$ is regular or biregular of class 1 (a biregular graph whose no two vertices of same degree are adjacent). There, it was also shown that there exist infinitely many connected graphs of maximal degree $\\Delta= 5$ that are neith"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1809","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"}