{"paper":{"title":"On the Domination Polynomials of Friendship Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jason Brown, Saeid Alikhani, Somayeh Jahari","submitted_at":"2014-01-08T16:30:57Z","abstract_excerpt":"Let $G$ be a simple graph of order $n$. The {\\em domination polynomial} of $G$ is the polynomial ${D(G, x)=\\sum_{i=0}^{n} d(G,i) x^{i}}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$.\n  Let $n$ be any positive integer and $F_n$ be the Friendship graph with $2n + 1$ vertices and $3n$ edges, formed by the join of $K_{1}$ with $nK_{2}$. We study the domination polynomials of this family of graphs, and in particular examine the domination roots of the family, and find the limiting curve for the roots. We also show that for every $n\\geq 2$, $F_n$ is not $\\mathcal{D}$-unique, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2092","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"}