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In an oft-cited paper \\cite{Akers:Krishnamurthy:1989} (see also \\cite{Hahn:Sabidussi:1997}), it is shown that the diameter of the Cayley graph $\\Gamma$ is bounded as $$\\diam(\\Gamma) \\le \\max_{\\pi \\in S_n}{c(\\pi)-n+\\sum_{i=1}^n \\dist_T(i,\\pi(i))},$$ where the maximization is over all permutations $\\pi$, $c(\\pi)$ denotes the number of cycles in $\\pi$, and $\\dist_T$ is the distance function in $T$. In this work, we first assess the performance (the sharpness and strictness) of this upper"},"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":"1111.3114","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-11-14T07:07:51Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"2d20ac2e4ff61214b226a6bc684614554aa53e90c90ebea13eefd12b7428ea40","abstract_canon_sha256":"8f50b24e9327417e416f4a4e1bd601b5adb6e9d0b48f30330a03f3dbde2b2f7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:38.897486Z","signature_b64":"NXaOyRm2NSys+bzjlvs4Hq/U6PN/rJS6xQIZNkp6R8wO1ZPTEJ2u20K+W5T5Xvl9g4CWBo9R5QcY56+IN2XrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3df4a7268894876e76e98e01404af45d4213039400fd3d7dfdc68cca82df87d","last_reissued_at":"2026-05-18T01:24:38.897002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:38.897002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diameter of Cayley graphs of permutation groups generated by transposition trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Ashwin Ganesan","submitted_at":"2011-11-14T07:07:51Z","abstract_excerpt":"Let $\\Gamma$ be a Cayley graph of the permutation group generated by a transposition tree $T$ on $n$ vertices. 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