{"paper":{"title":"Distance-regular graphs with classical parameters that support a uniform structure: case $q \\le 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Blas Fern\\'andez, Giusy Monzillo, Roghayeh Maleki, \\v{S}tefko Miklavi\\v{c}","submitted_at":"2023-05-15T18:18:48Z","abstract_excerpt":"Let $\\Gamma=(X,\\mathcal{R})$ denote a finite, simple, connected, and undirected non-bipartite graph with vertex set $X$ and edge set $\\mathcal{R}$. Fix a vertex $x \\in X$, and define $\\mathcal{R}_f = \\mathcal{R} \\setminus \\{yz \\mid \\partial(x,y) = \\partial(x,z)\\}$, where $\\partial$ denotes the path-length distance in $\\Gamma$. Observe that the graph $\\Gamma_f=(X,\\mathcal{R}_f)$ is bipartite. We say that $\\Gamma$ supports a uniform structure with respect to $x$ whenever $\\Gamma_f$ has a uniform structure with respect to $x$.\n  Assume that $\\Gamma$ is a distance-regular graph with classical para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08937","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/2305.08937/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"}