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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("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.0075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-01T11:25:08Z","cross_cats_sorted":[],"title_canon_sha256":"63893533bd36aa9e51b4572e9fee9d8ef950826c7503f8a82be4acdcee501d23","abstract_canon_sha256":"9f62858a01d6201d7cb0eff5a92c70ddd29f31d4d73f7e02995cabbb83feb128"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:28.334256Z","signature_b64":"fEldv/Skg6BQ69MfbwPQ8Lx31xWSn+vFIwOP2aroR4uAna1wKIOcHvhfe2njeihNAx1GnuJW82GbYoAayiXZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9324a77ca1642c13fedcebaf9ed0fbf6bca98e412a1e77bd1c4aff5f6d19cba","last_reissued_at":"2026-05-18T03:37:28.333669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:28.333669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.0075","created_at":"2026-05-18T03:37:28.333769+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0075v1","created_at":"2026-05-18T03:37:28.333769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0075","created_at":"2026-05-18T03:37:28.333769+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EZEU56KCZBM","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EZEU56KCZBMCP7N","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EZEU56K","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5","json":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5.json","graph_json":"https://pith.science/api/pith-number/3EZEU56KCZBMCP7NZ25PT3IPX5/graph.json","events_json":"https://pith.science/api/pith-number/3EZEU56KCZBMCP7NZ25PT3IPX5/events.json","paper":"https://pith.science/paper/3EZEU56K"},"agent_actions":{"view_html":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5","download_json":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5.json","view_paper":"https://pith.science/paper/3EZEU56K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0075&json=true","fetch_graph":"https://pith.science/api/pith-number/3EZEU56KCZBMCP7NZ25PT3IPX5/graph.json","fetch_events":"https://pith.science/api/pith-number/3EZEU56KCZBMCP7NZ25PT3IPX5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5/action/storage_attestation","attest_author":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5/action/author_attestation","sign_citation":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5/action/citation_signature","submit_replication":"https://pith.science/pith/3EZEU56KCZBMCP7NZ25PT3IPX5/action/replication_record"}},"created_at":"2026-05-18T03:37:28.333769+00:00","updated_at":"2026-05-18T03:37:28.333769+00:00"}