{"paper":{"title":"Complexity of circulant graphs with non-fixed jumps, its arithmetic properties and asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Mednykh, Ilya Mednykh","submitted_at":"2018-12-10T02:34:00Z","abstract_excerpt":"In the present paper, we investigate a family of circulant graphs with non-fixed jumps $$G_n=C_{\\beta n}(s_1, \\ldots,s_k,\\alpha_1n,\\ldots,\\alpha_\\ell n),\\, 1\\le s_1<\\ldots<s_k\\le[\\frac{\\beta n}{2}],\\, 1\\le \\alpha_1< \\ldots<\\alpha_\\ell\\le[\\frac{\\beta}{2}].$$ Here $n$ is an arbitrary large natural number and integers $s_1, \\ldots,s_k,\\alpha_1, \\ldots,\\alpha_\\ell$ are supposed to be fixed.\n  First, we present an explicit formula for the number of spanning trees in the graph $G_n.$ This formula is a product of $\\beta s_k-1$ factors, each given by the $n$-th Chebyshev polynomial of the first kind e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04484","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"}