{"paper":{"title":"Degree distributions for a class of Circulant graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dongseok Kim, Jaeun Lee, Young Soo Kwon","submitted_at":"2014-02-15T02:00:56Z","abstract_excerpt":"We characterize the equivalence and the weak equivalence of Cayley graphs for a finite group $\\C{A}$. Using these characterizations, we find degree distribution polynomials for weak equivalence of some graphs including 1) circulant graphs of prime power order, 2) circulant graphs of order $4p$, 3) circulant graphs of square free order and 4) Cayley graphs of order $p$ or $2p$. As an application, we find an enumeration formula for the number of weak equivalence classes of circulant graphs of prime power order, order $4p$ and square free order and Cayley graphs of order $p$ or $2p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3635","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"}