{"paper":{"title":"Cospectral mates for the union of some classes in the Johnson association scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Matt McGinnis, Sebastian M. Cioab\\u{a}, Travis Johnston, Willem H. Haemers","submitted_at":"2017-01-30T18:36:00Z","abstract_excerpt":"Let $n\\geq k\\geq 2$ be two integers and $S$ a subset of $\\{0,1,\\dots,k-1\\}$. The graph $J_{S}(n,k)$ has as vertices the $k$-subsets of the $n$-set $[n]=\\{1,\\dots,n\\}$ and two $k$-subsets $A$ and $B$ are adjacent if $|A\\cap B|\\in S$. In this paper, we use Godsil-McKay switching to prove that for $m\\geq 0$, $k\\geq \\max(m+2,3)$ and $S = \\{0, 1, ..., m\\}$, the graphs $J_S(3k-2m-1,k)$ are not determined by spectrum and for $m\\geq 2$, $n\\geq 4m+2$ and $S = \\{0,1,...,m\\}$ the graphs $J_{S}(n,2m+1)$ are not determined by spectrum. We also report some computational searches for Godsil-McKay switching s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08747","kind":"arxiv","version":2},"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"}