{"paper":{"title":"On the Mean Connected Induced Subgraph Order of Cographs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Mol, Matthew E. Kroeker, Ortrud R. Oellermann","submitted_at":"2017-08-06T17:39:24Z","abstract_excerpt":"In this article the extremal structures for the mean order of connected induced subgraphs of cographs are determined. It is shown that among all connected cographs of order $n \\ge 7$, the star $K_{1,n-1}$ has maximum mean connected induced subgraph order, and for $n \\ge 3$, the $n$-skillet, $K_1+(K_1 \\cup K_{n-2})$, has minimum mean connected induced subgraph order. It is deduced that the density for connected cographs (i.e. the ratio of the mean to the order of the graph) is asymptotically $1/2$. The mean order of all connected induced subgraphs containing a given vertex $v$ of a cograph $G$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01916","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"}