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Bipartite graphs of order $\\M^b(d,D)$ are very rare, and determining $\\N^b(d,D)$ still remains an open problem for most $(d,D)$ pairs.\n  This paper is a follow-up to our earlier paper \\cite{FPV12}, where a study on bipartite $(d,D,-4)$-graphs (that is, bipartite "},"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":"1203.3588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-15T23:10:30Z","cross_cats_sorted":[],"title_canon_sha256":"4cef8ef5a6b2aa9edc9472a805aa3feb4c14489ed71d8e4eca7de844e3a59433","abstract_canon_sha256":"fed562a7b3b05fa3dce61fa7e7d03fdeec720c3e9abd99c1a636315a6bd2ad80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:42.398500Z","signature_b64":"z/GHcCGD1FxmlBQ1D4hI/3uDy3UiDdSv88bypglKQw223znqrhin8Dz0j7bSqOWrkOk4ae+QIzi0zAtM425YCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d8028b02611c747ff47e420dbe953ca294415f4c125c0ba0f9b1c17d7225141","last_reissued_at":"2026-05-18T02:52:42.398050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:42.398050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On large bipartite graphs of diameter 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guillermo Pineda-Villavicencio, Mirka Miller, Ramiro Feria-Puron","submitted_at":"2012-03-15T23:10:30Z","abstract_excerpt":"We consider the bipartite version of the {\\it degree/diameter problem}, namely, given natural numbers $d\\ge2$ and $D\\ge2$, find the maximum number $\\N^b(d,D)$ of vertices in a bipartite graph of maximum degree $d$ and diameter $D$. 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