{"paper":{"title":"Laplacian eigenvalues of the zero divisor graph of the ring $\\mathbb{Z}_{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SP","authors_text":"Binod Kumar Sahoo, Kamal Lochan Patra, Sriparna Chattopadhyay","submitted_at":"2019-03-19T05:19:10Z","abstract_excerpt":"We study the Laplacian eigenvalues of the zero divisor graph $\\Gamma\\left(\\mathbb{Z}_{n}\\right)$ of the ring $\\mathbb{Z}_{n}$ and prove that $\\Gamma\\left(\\mathbb{Z}_{p^t}\\right)$ is Laplacian integral for every prime $p$ and positive integer $t\\geq 2$. We also prove that the Laplacian spectral radius and the algebraic connectivity of $\\Gamma\\left(\\mathbb{Z}_{n}\\right)$ for most of the values of $n$ are, respectively, the largest and the second smallest eigenvalues of the vertex weighted Laplacian matrix of a graph which is defined on the set of proper divisors of $n$. The values of $n$ for whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07841","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"}