{"paper":{"title":"The total irregularity of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Darko Dimitrov, Hosam Abdo","submitted_at":"2012-07-22T23:27:20Z","abstract_excerpt":"In this note a new measure of irregularity of a simple undirected graph $G$ is introduced. It is named the total irregularity of a graph and is defined as $\\irr_t(G) = 1/2\\sum_{u,v \\in V(G)} |d_G(u)-d_G(v)|$, where $d_G(u)$ denotes the degree of a vertex $u \\in V(G)$. The graphs with maximal total irregularity are determined. It is also shown that among all trees of same order the star graph has the maximal total irregularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5267","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"}