{"paper":{"title":"A note on $f^\\pm$-Zagreb indices in respect of Jaco Graphs, $J_n(1), n \\in \\Bbb N$ and the introduction of Khazamula irregularity","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johan Kok, Vivian Mukungunugwa","submitted_at":"2014-07-31T06:34:57Z","abstract_excerpt":"The topological indices $irr(G)$ related to the \\emph{first Zagreb index,} $M_1(G)$ and the \\emph{second Zagreb index,} $M_2(G)$ are the oldest irregularity measures researched. Alberton $[3]$ introduced the \\emph{irregularity} of $G$ as $irr(G) = \\sum\\limits_{e \\in E(G)}imb(e), imb(e) = |d(v) - d(u)|_{e=vu}$. In the paper of Fath-Tabar $[7]$, Alberton's indice was named the \\emph{third Zagreb indice} to conform with the terminology of chemical graph theory. Recently Ado et.al. $[1]$ introduced the topological indice called \\emph{total irregularity}. The latter could be called the \\emph{fourth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8290","kind":"arxiv","version":3},"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"}