{"paper":{"title":"Half-arc-transitive graphs of arbitrary even valency greater than 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arjana \\v{Z}itnik, Marston D.E. Conder","submitted_at":"2015-05-09T18:12:02Z","abstract_excerpt":"A half-arc-transitive graph is a regular graph that is both vertex- and edge-transitive, but is not arc-transitive. If such a graph has finite valency, then its valency is even, and greater than $2$. In 1970, Bouwer proved that there exists a half-arc-transitive graph of every even valency greater than 2, by giving a construction for a family of graphs now known as $B(k,m,n)$, defined for every triple $(k,m,n)$ of integers greater than $1$ with $2^m \\equiv 1 \\mod n$. In each case, $B(k,m,n)$ is a $2k$-valent vertex- and edge-transitive graph of order $mn^{k-1}$, and Bouwer showed that $B(k,6,9"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02299","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"}