{"paper":{"title":"Metacirculants and split weak metacirculants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Jin-Xin Zhou, Li Cui","submitted_at":"2018-04-05T00:33:08Z","abstract_excerpt":"Metacirculants are a rich resource of many families of interesting graphs, and weak metacirculants are generalizations of them. A graph is called a {\\em split weak metacirculant} if it has a vertex-transitive split metacyclic automorphism group. In two recent papers, it is shown that a graph of prime power order is a metacirculant if and only if it is a split weak metacirculant. Let $m$ is a positive integer. In this paper, we first give a sufficient condition for the existence of split weak metacirculants of order $m$ which are not metacirculants. This is then used to give a sufficient and ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01632","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"}