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We define two types of operators. For the first one, let $v$ be a vertex of $G$ and $a\\in \\mathbf{F}_q$, and obtain the graph with labels $g'_{ij}=g_{ij}+ag_{vi}g_{vj}$. For the second, if $0\\neq b\\in \\mathbf{F}_q$ the resulted graph is a graph with labels $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":"cs/0702057","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.DS","submitted_at":"2007-02-09T15:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"acfe26e993f2839cd1343dee08b2746ba8978b0fd606d331f09fb6a298a5c0c8","abstract_canon_sha256":"cdcbc36a19d26bdabd8bd60adb13ba4502073ab7f7ad83c2e4a2274facf8e612"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:02:31.302508Z","signature_b64":"ZHalKCbCONQIePxN3DkLCoOIIMxbXvDD/unORjxgFkIXBIWPlt5lZVFxnl/pUHWf33nkt5EYPX+HzZAcp2yUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5f73bd2a26dfc7cefd1e37fcc87e6ac8c5946a1ff153d07e359425b5345adad","last_reissued_at":"2026-07-04T15:02:31.302137Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:02:31.302137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Efficient Algorithm to Recognize Locally Equivalent Graphs in Non-Binary Case","license":"","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mohsen Bahramgiri, Salman Beigi","submitted_at":"2007-02-09T15:42:46Z","abstract_excerpt":"Let $v$ be a vertex of a graph $G$. 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