{"paper":{"title":"Vertex connectivity of the power graph of a finite cyclic group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binod Kumar Sahoo, Kamal Lochan Patra, Sriparna Chattopadhyay","submitted_at":"2017-03-21T11:09:00Z","abstract_excerpt":"Let $n=p_1^{n_1}p_2^{n_2}\\ldots p_r^{n_r}$, where $r,n_1,\\ldots, n_r$ are positive integers and $p_1,p_2,\\ldots,p_r$ are distinct prime numbers with $p_1<p_2<\\cdots <p_r$. For the cyclic group $C_n$ of order $n$, let $\\mathcal{P}(C_n)$ be the power graph of $C_n$ and $\\kappa(\\mathcal{P}(C_n))$ be the vertex connectivity of $\\mathcal{P}(C_n)$. It is known that $\\kappa(\\mathcal{P}(C_n))=p_1^{n_1} -1$ if $r=1$. For $r\\geq 2$, we determine the exact value of $\\kappa(\\mathcal{P}(C_n))$ when $2\\phi(p_1\\ldots p_{r-1})\\geq p_1\\ldots p_{r-1}$, and give an upper bound for $\\kappa(\\mathcal{P}(C_n))$ when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07149","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"}