{"paper":{"title":"On basic graphs of symmetric graphs of valency five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Da-Wei Yang, Jaeun Lee, Jin Ho Kwak, Yan-Quan Feng","submitted_at":"2017-07-17T00:50:56Z","abstract_excerpt":"A graph $\\G$ is {\\em symmetric} or {\\em arc-transitive} if its automorphism group $\\Aut(\\G)$ is transitive on the arc set of the graph, and $\\G$ is {\\em basic} if $\\Aut(\\G)$ has no non-trivial normal subgroup $N$ such that the quotient graph $\\G_N$ has the same valency with $\\G$. In this paper, we classify symmetric basic graphs of order $2qp^n$ and valency 5, where $q<p$ are two primes and $n$ is a positive integer. It is shown that such a graph is isomorphic to a family of Cayley graphs on dihedral groups of order $2q$ with $5\\di (q-1)$, the complete graph $K_6$ of order $6$, the complete bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04969","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"}