{"paper":{"title":"Spectral characterization of mixed extensions of small graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Willem H. Haemers","submitted_at":"2017-12-05T16:40:32Z","abstract_excerpt":"A mixed extension of a graph $G$ is a graph $H$ obtained from $G$ by replacing each vertex of $G$ by a clique or a coclique, where vertices of $H$ coming from different vertices of $G$ are adjacent if and only if the original vertices are adjacent in $G$. If $G$ has no more than three vertices, $H$ has all but at most three adjacency eigenvalues equal to $0$ or $-1$. In this paper we consider the converse problem, and determine the class $\\cal G$ of all graphs with at most three eigenvalues unequal to $0$ and $-1$. Ignoring isolated vertices, we find that $\\cal G$ consists of all mixed extensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01749","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"}