{"paper":{"title":"On eigenvalues of Seidel matrices and Haemers' conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ebrahim Ghorbani","submitted_at":"2013-01-01T11:25:08Z","abstract_excerpt":"For a graph $G$, let $S(G)$ be the Seidel matrix of $G$ and $\\te_1(G),...,\\te_n(G)$ be the eigenvalues of $S(G)$. The Seidel energy of $G$ is defined as $|\\te_1(G)|+...+|\\te_n(G)|$. Willem Haemers conjectured that the Seidel energy of any graph with $n$ vertices is at least $2n-2$, the Seidel energy of the complete graph with $n$ vertices. Motivated by this conjecture, we prove that for any $\\al$ with $0<\\al<2$, $|\\te_1(G)|^\\al+...+|\\te_n(G)|^\\al\\g (n-1)^\\al+n-1$ if and only if $|{\\rm det} S(G)|\\g n-1$. This, in particular, implies the Haemers' conjecture for all graphs $G$ with $|{\\rm det} S("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0075","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"}