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We give a necessary and sufficient condition for the lexicographic product of two graphs to be a dp graph. A graph $G$ is $sequentially\\ distance\\ preserving\\ (sdp)$ if the vertex set of $G$ can be ordered so that, for all $i\\ge1$, deleting the first $i$ vertices in the sequence results in an isometric g"},"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":"1507.04800","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T23:41:36Z","cross_cats_sorted":[],"title_canon_sha256":"a17211465bb854b2b3340554047c758cd6209da02a4473a1db7163d141c807e3","abstract_canon_sha256":"25f1963f2dd7ed8b1115a4a772b71507662dd67d59b8a36f51bb78ef52b3ef69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:00.128844Z","signature_b64":"lPH7NEkyTEEp+FLeDb6V3UmwohJ09kwBV8w2ox+HMCJPokchsk5iasvHTFix3tpxSOTz0TAgsUbPbqOyEvIXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b59782c9519a5ff06449a7a9dc7c91db7386f91c4ba0797e87fefdd6f7e2668","last_reissued_at":"2026-05-18T01:27:00.128086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:00.128086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distance preserving graphs and graph products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruce E. 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