{"paper":{"title":"On Mean Distance and Girth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Mekkia Kouider, Siham Bekkai","submitted_at":"2008-06-09T12:15:28Z","abstract_excerpt":"We bound the mean distance in a connected graph which is not a tree in function of its order $n$ and its girth $g$. On one hand, we show that mean distance is at most $\\frac{n+1}{3}-\\frac{g(g^2-4)}{12n(n-1)}$ if $g$ is even and at most $\\frac{n+1}{3}-\\frac{g(g^2-1)}{12n(n-1)}$ if $g$ is odd. On the other hand, we prove that mean distance is at least $\\frac{ng}{4(n-1)}$ unless $G$ is an odd cycle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1438","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"}