{"paper":{"title":"Maximizing the algebraic connectivity of graphs of given order and size: a proof of a conjecture of Kolokolnikov","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhay Jayarajan, M. Rajesh Kannan, Rahul Roy, Sebastian M. Cioab\\u{a}","submitted_at":"2026-08-10T17:32:53Z","abstract_excerpt":"The algebraic connectivity of a graph $G$ is a well studied graph invariant that is related to other properties of the graph such as connectivity and expansion. Given $n$ and $m$, $\\alpha(n,m)$ is the maximum algebraic connectivity of a graph with $n$ vertices with $m$ edges. In 2015, Kolokolnikov conjectured that $\\alpha(n,2n-4)=2$ for $n\\geq 3$, and verified this claim computationally for $n \\le 12$. In this paper, we prove Kolokolnikov's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09879","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.09879/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}