{"paper":{"title":"Affine flag graphs and classification of a family of symmetric graphs with complete quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Sanming Zhou, Teng Fang, Yu Qing Chen","submitted_at":"2019-08-04T05:01:16Z","abstract_excerpt":"A graph $\\Gamma$ is $G$-symmetric if $G$ is a group of automorphisms of $\\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\\Gamma$. If $V(\\Gamma)$ admits a nontrivial $G$-invariant partition ${\\cal B}$ such that for blocks $B, C \\in {\\cal B}$ adjacent in the quotient graph $\\Gamma_{{\\cal B}}$ of $\\Gamma$ relative to ${\\cal B}$, exactly one vertex of $B$ has no neighbour in $C$, then $\\Gamma$ is called an almost multicover of $\\Gamma_{{\\cal B}}$. In this case an incidence structure with point set ${\\cal B}$ arises naturally, and it is a $(G, 2)$-point-transitive a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01273","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01273/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}