{"paper":{"title":"A note on the augmented Zagreb index of cacti with fixed number of vertices and cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akbar Ali, Akhlaq Ahmad Bhatti","submitted_at":"2016-05-06T10:55:57Z","abstract_excerpt":"Let $\\mathcal{C}_{n,k}$ be the family of all cacti with $k$ cycles and $n\\geq4$ vertices. In the present note, the element of the class $\\mathcal{C}_{n,k}$ having minimum augmented Zagreb index ($AZI$) is characterized. Moreover, some structural properties of the graph(s) having maximum $AZI$ value over the collection $\\mathcal{C}_{n,0}$, are also reported."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01888","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"}