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For a pair of graphs $(C, P)$ the central-peripheral appendage number, $A_{ucg}(C, P)$, is the minimum number verticies needed to be adjoined to the graphs $C$ and $P$ in order to construct a uniform central graph H with center C and centered-periphery P. We compute $A_{ucg}(C, P)$ in terms of the radius and diameter of P and whether or not $C$ is a complete graph. In the process we show $A_{ucg}(C, P)\\leq 6$ if $d"},"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":"1705.07982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-22T20:18:06Z","cross_cats_sorted":[],"title_canon_sha256":"f1f1738cb0b6cbd0ce1811a4f21a9b03f78658d9901b48141e2b1fabca41d9e1","abstract_canon_sha256":"95a5cc77d2b198c09f0a40119b92a43f30003f088a129a0108b3d14e5e48b179"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:03.983541Z","signature_b64":"Bn0CKSmFn9cdDW9+aCLs9yFZFx5+hihrjQiS2WncmWx72iJKNgfG5NkMPT5LHMfe9wiC/e2xUL/0B0+4STs0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4155562283dc36f29a0b5215a9707fe51ee7d4b7f7e787743bde5b6050440132","last_reissued_at":"2026-05-18T00:44:03.983051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:03.983051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Central-Peripheral Appendage Numbers of Uniform Central Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonathan Needleman, Sul-Young Choi","submitted_at":"2017-05-22T20:18:06Z","abstract_excerpt":"In a uniform central graph (UCG) the eccentric verticies of a central vertex is the same for all central verticies. This collection of eccentric verticies is the centered periphery. For a pair of graphs $(C, P)$ the central-peripheral appendage number, $A_{ucg}(C, P)$, is the minimum number verticies needed to be adjoined to the graphs $C$ and $P$ in order to construct a uniform central graph H with center C and centered-periphery P. We compute $A_{ucg}(C, P)$ in terms of the radius and diameter of P and whether or not $C$ is a complete graph. 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