{"paper":{"title":"The minimum rank of universal adjacency matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Bahman Ahmadi, Fatemeh Alinaghipour, Karen Meagher, Shahla Nasserasr, Shaun M. Fallat, Yi-Zheng Fan","submitted_at":"2011-12-07T22:22:44Z","abstract_excerpt":"In this paper we introduce a new parameter for a graph called the {\\it minimum universal rank}. This parameter is similar to the minimum rank of a graph. For a graph $G$ the minimum universal rank of $G$ is the minimum rank over all matrices of the form \\[ U(\\alpha, \\beta, \\gamma, \\delta) = \\alpha A + \\beta I + \\gamma J + \\delta D \\] where $A$ is the adjacency matrix of $G$, $J$ is the all ones matrix and $D$ is the matrix with the degrees of the vertices in the main diagonal, and $\\alpha\\neq 0, \\beta, \\gamma, \\delta$ are scalars. Bounds for general graphs based on known graph parameters are g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1718","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"}