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Answering a question of Havet, H\\\"orsch and Rambaud, we prove the bound in terms of edge number $\\diam(I(G)) \\le 2\\sqrt{|E(G)|}$, and we complement it with a lower bound $\\diam(I(G)) \\ge \\frac{|E(G)|}{|V(G)|}$ obtained by viewing $I(G)$ as a Cayley gra"},"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":"2606.17974","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T14:28:59Z","cross_cats_sorted":[],"title_canon_sha256":"20b64c80d29526f43b89b2a8bcddf150a271e3b49fcad4272aafb61444508e6d","abstract_canon_sha256":"0f94db5cf6353b6a0c45ce6bb1b74015633ccc5f970fc5f7bd26a44469d1471d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:44.927280Z","signature_b64":"v+NXWfI4EqFn5dWYhgMu9gOIg4szUE3x75e4g4WoEDdnZ79HC9wkCgfU1mtnZy0CGFpBGk/yMf4uc2TgMaAtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33de6cd60316c8c7486781085071342118fe8a815b4c69c006e3a2ab8a96896c","last_reissued_at":"2026-06-19T16:10:44.926940Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:44.926940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge-Number Bounds for the Inversion Diameter of Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anqi Li, Jiawen Bo, Xiaopan Lian, Xin Yan","submitted_at":"2026-06-16T14:28:59Z","abstract_excerpt":"The inversion of a set $X$ of vertices in an oriented graph reverses every arc with both endpoints in $X$. 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