{"paper":{"title":"Some families of graphs whose domination polynomials are unimodal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Saeid Alikhani, Somayeh Jahari","submitted_at":"2014-01-06T18:05:12Z","abstract_excerpt":"Let $G$ be a simple graph of order $n$.\nThe domination polynomial of $G$ is the polynomial\n$D(G, x)=\\sum_{i=\\gamma(G)}^{n} d(G,i) x^{i}$,\nwhere $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and\n$\\gamma(G)$ is the domination number of $G$.  It is conjectured that the domination polynomial of any graph is unimodal.\nIn this paper we present  some  families of graphs whose domination polynomials are unimodal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1159","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"}