{"paper":{"title":"The Minimal Total Irregularity of Graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jieshan Yang, Lihua You, Yingxue Zhu","submitted_at":"2014-04-03T14:26:20Z","abstract_excerpt":"In \\cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph $G=(V,E)$ as\n  \\hskip3.3cm $\\rm irr_{t}$$(G) = \\frac{1}{2}\\sum_{u,v\\in V}|d_{G}(u)-d_{G}(v)|, $\n  \\noindent where $d_{G}(u)$ denotes the vertex degree of a vertex $u\\in V$. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on $n$ vertices, and propose an open problem for further research."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0931","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"}