{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BFK3BXVGE74UF6PWZO53ASDOI5","short_pith_number":"pith:BFK3BXVG","schema_version":"1.0","canonical_sha256":"0955b0dea627f942f9f6cbbbb0486e47733dfbe79fa53479ed6bf33ff575c924","source":{"kind":"arxiv","id":"1211.0910","version":1},"attestation_state":"computed","paper":{"title":"Biregular cages of girth five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Balbuena, D. Labbate, G. Araujo-Pardo, G. Lopez-Chavez, M. Abreu","submitted_at":"2012-11-05T16:21:56Z","abstract_excerpt":"Let $2 \\le r < m$ and $g$ be positive integers. An $({r,m};g)$--graph} (or biregular graph) is a graph with degree set ${r,m}$ and girth $g$, and an $({r,m};g)$-cage (or biregular cage) is an $({r,m};g)$-graph of minimum order $n({r,m};g)$. If $m=r+1$, an $({r,m};g)$-cage is said to be a semiregular cage.\n  In this paper we generalize the reduction and graph amalgam operations from M. Abreu, G. Araujo-Pardo, C. Balbuena, D. Labbate (2011) on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. The construct"},"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":"1211.0910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-05T16:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"953c8cb05e4f7a3b15cbd6a1b1a6587deddf798be961415c418c93eaedf9fa35","abstract_canon_sha256":"2909a8071f9cf80643c76836dc65a9bd9326a9790757087972c09765d247df49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:39.368678Z","signature_b64":"YXHWtlp213ZwUDxE6W6FTwXUXDYdG4Nr3TknfiHQ0hKLE0ZjpoYZpRT9IsohVjoNHFGojOWxUZeOCq/i1qk3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0955b0dea627f942f9f6cbbbb0486e47733dfbe79fa53479ed6bf33ff575c924","last_reissued_at":"2026-05-18T02:29:39.368139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:39.368139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biregular cages of girth five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Balbuena, D. Labbate, G. Araujo-Pardo, G. Lopez-Chavez, M. Abreu","submitted_at":"2012-11-05T16:21:56Z","abstract_excerpt":"Let $2 \\le r < m$ and $g$ be positive integers. An $({r,m};g)$--graph} (or biregular graph) is a graph with degree set ${r,m}$ and girth $g$, and an $({r,m};g)$-cage (or biregular cage) is an $({r,m};g)$-graph of minimum order $n({r,m};g)$. If $m=r+1$, an $({r,m};g)$-cage is said to be a semiregular cage.\n  In this paper we generalize the reduction and graph amalgam operations from M. Abreu, G. Araujo-Pardo, C. Balbuena, D. Labbate (2011) on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. 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