{"paper":{"title":"Bipartite graphs with five eigenvalues and pseudo designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ebrahim Ghorbani","submitted_at":"2009-05-17T14:00:46Z","abstract_excerpt":"A pseudo $(v,\\, k,\\, \\la)$-design is a pair $(X, {\\cal B})$ where $X$ is a $v$-set and ${\\cal B}=\\{B_1,...,B_{v-1}\\}$ is a collection of $k$-subsets (blocks) of $X$ such that each two distinct $B_i, B_j$ intersect in $\\la$ elements; and $0\\le\\la <k \\le v-1$. We use the notion of pseudo designs to characterize graphs of order $n$ whose (adjacency) spectrum contains a zero and $\\pm\\theta$ with multiplicity $(n-3)/2$ where $0<\\theta\\le\\sqrt{2}$. Meanwhile, partial results confirming a conjecture of O. Marrero on characterization of pseudo $(v,\\, k,\\, \\la)$-designs are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2740","kind":"arxiv","version":3},"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"}