{"paper":{"title":"Sum of squares of degrees in a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernardo M. \\'Abrego, Michael G. Neubauer, Silvia Fern\\'andez-Merchant, William Watkins","submitted_at":"2008-08-16T03:27:11Z","abstract_excerpt":"Let $\\G(v,e)$ be the set of all simple graphs with $v$ vertices and $e$ edges and let $P_2(G)=\\sum d_i^2$ denote the sum of the squares of the degrees, $d_1, >..., d_v$, of the vertices of $G$.\n  It is known that the maximum value of $P_2(G)$ for $G \\in \\G(v,e)$ occurs at one or both of two special graphs in $\\G(v,e)$--the \\qs graph or the \\qc graph. For each pair $(v,e)$, we determine which of these two graphs has the larger value of $P_2(G)$. We also determine all pairs $(v,e)$ for which the values of $P_2(G)$ are the same for the \\qs and the \\qc graph. In addition to the \\qs and \\qc graphs,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2234","kind":"arxiv","version":2},"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"}