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If $n>400t^{6}$, then the spectral radius $\\mu\\left( G\\right) $ satisfies \\[ \\mu\\left( G\\right) \\leq\\frac{t-1}{2}+\\sqrt{n+\\frac{t^{2}-2t-3}{4}}, \\] with equality if and only if $n\\equiv1$ $(\\operatorname{mod}$ $t)$ and $G=K_{1}\\vee\\left\\lfloor n/t\\right\\rfloor K_{t}$.\n  For $t=3$ the maximum $\\mu\\left( G\\right) $ is found exactly for any $n>40000$."},"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":"1703.01839","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-06T12:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"4b4d545b4be758c8fa64ffd91527b7985544afa97f0db35e6bdd945da565b456","abstract_canon_sha256":"3d7acda6fe62c6f270263bc3a8ce9e9c3e9625e298b83f88fc1c484d13a369c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:29.542681Z","signature_b64":"TIzwXfjMuNseVnvzFLwsUB1wOGt2OjY0pbPBu3YGHuRFKbGn+CXbD+W3VjDvTsKYIc+wP6GzlD0jBerBHwcAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbcbcde71ea30009ba60713b3d1076110f9a572aeef07f0efd9bd454f79f3962","last_reissued_at":"2026-05-18T00:49:29.541973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:29.541973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The spectral radius of graphs with no $K_{2,t}$ minor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"V. 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