{"paper":{"title":"Hangable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Jerzy Topp, Mateusz Miotk","submitted_at":"2015-12-24T09:31:14Z","abstract_excerpt":"Let $G=(V_G,E_G)$ be a connected graph. The distance $d_G(u,v)$ between vertices $u$ and $v$ in $G$ is the length of a shortest $u-v$ path in $G$. The eccentricity of a vertex $v$ in $G$ is the integer $e_G(v)= \\max\\{ d_G(v,u) \\colon u\\in V_G\\}$. The diameter of $G$ is the integer $d(G)= \\max\\{e_G(v)\\colon v\\in V_G\\}$. The periphery of a~vertex $v$ of $G$ is the set $P_G(v)= \\{u\\in V_G\\colon d_G(v,u)= e_G(v)\\}$, while the periphery of $G$ is the set $P(G)= \\{v\\in V_G\\colon e_G(v)=d(G)\\}$. We say that graph $G$ is hangable if $P_G(v)\\subequal P(G)$ for every vertex $v$ of $G$. In this paper we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07767","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"}