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The monomial digraph $D= D(q;m,n)$ is defined as follows: the vertex set of $D$ is $\\mathbb{F}_q^2$, and $((x_1,x_2),(y_1,y_2))$ is an arc in $D$ if $ x_2 + y_2 = x_1^m y_1^n $. In this note we study the question of isomorphism of monomial digraphs $D(q;m_1,n_1)$ and $D(q;m_2,n_2)$. Several necessary conditions and several sufficient conditions for the isomorphism are found. We conjecture that one simple sufficient condition is also"},"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":"1807.11362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T14:12:20Z","cross_cats_sorted":[],"title_canon_sha256":"98bae4000a48907836cd87579da0da1b4b6d99197ee3f246d3c787102145faef","abstract_canon_sha256":"9926b92904b2262ad3986e6c75d219286532d588eabb51a94966e8d0af140f86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.102652Z","signature_b64":"AGXgRqBz2nv7sjobZre4FUXk1JO2xBxbEyTgvDq8rz0gb71jCZl7ztYDWsXQM1NeFFYrEDRN/+RxFuhuVn0tAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adf386c808f871568180754c94d82c92adee559142c4deaf07a14c0a0ad26380","last_reissued_at":"2026-05-18T00:09:32.102103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.102103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on the Isomorphism Problem for Monomial Digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Kodess, Felix Lazebnik","submitted_at":"2018-07-30T14:12:20Z","abstract_excerpt":"Let $p$ be a prime $e$ be a positive integer, $q = p^e$, and let $\\mathbb{F}_q$ denote the finite field of $q$ elements. 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