{"paper":{"title":"A spectral characterization of the s-clique extension of the square grid graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack H. Koolen, Muhammad Riaz, Sakander Hayat","submitted_at":"2018-06-10T06:34:01Z","abstract_excerpt":"In this paper we show that for integers $s\\geq2$, $t\\geq1$, any co-edge-regular graph which is cospectral with the $s$-clique extension of the $t\\times t$-grid is the $s$-clique extension of the $t\\times t$-grid, if $t$ is large enough. Gavrilyuk and Koolen used a weaker version of this result to show that the Grassmann graph $J_q(2D,D)$ is characterized by its intersection array as a distance-regular graph, if $D$ is large enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03593","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"}