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We prove that for any graph $G$, $\\kappa'(G\\times H)=\\textup{min}\\{2\\kappa'(G)e(H),\\delta(G)\\delta(H)\\}$, where $e(H)$ denotes the number of edges in $H$. In addition, the structure of minimum edge cuts is described. As an application, we present a necessary and sufficient condition for $G\\times K_n(n\\ge3)$ to be super edge connected."},"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":"1102.5181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T07:58:03Z","cross_cats_sorted":[],"title_canon_sha256":"d74603c797c90ea3b7f3b33127a0a54e5c9b5269ea2f5f44b8d0f3ba5c44eac3","abstract_canon_sha256":"4599381528a03fd0726abddd11661327493c076aaa66aa9c399f70d5468e6132"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:56.117744Z","signature_b64":"Q3CDNO/Ggd2SnVhwVZXEnHDFdUfIkppWAaBCh+YWJlhFg3VKn6i0Wsfrm70Zi2OTRQhecG+cUupYsBVazkRjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c9af64ffda7382cb54d7aa19456aeffd2e1d2f32cd907d297fab0bfd248c866","last_reissued_at":"2026-05-18T04:27:56.117083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:56.117083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the edge connectivity of direct products with dense graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wei Wang, Zhidan Yan","submitted_at":"2011-02-25T07:58:03Z","abstract_excerpt":"Let $\\kappa'(G)$ be the edge connectivity of $G$ and $G\\times H$ the direct product of $G$ and $H$. 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