{"paper":{"title":"The bondage number of graphs on topological surfaces: degree-S vertices and the average degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladimir Samodivkin","submitted_at":"2013-05-24T11:32:59Z","abstract_excerpt":"The bondage number $b(G)$ of a graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with larger domination number. An orientable surface $\\mathbb{S}_h$ of genus $h$, $h \\geq 0$, is obtained from the sphere $\\mathbb{S}_0$ by adding $h$ handles. A non-orientable surface $\\mathbb{N}_q$ of genus $q$, $q \\geq 1$, is obtained from the sphere by adding $q$ crosscaps. The Euler characteristic of a surface is defined by $\\chi(\\mathbb{S}_h) = 2 - 2h$ and $\\chi(\\mathbb{S}_q)= 2-q$. Let $G$ be a connected graph of order $n$ which is 2-cell embedded on a surface $\\mathbb{M}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5692","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"}