{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UWRAQCYGVOVEVBLMJJIL6NUKWG","short_pith_number":"pith:UWRAQCYG","schema_version":"1.0","canonical_sha256":"a5a2080b06abaa4a856c4a50bf368ab1aa48851f6f4a87d86503d3f93b0a3d25","source":{"kind":"arxiv","id":"1507.05306","version":1},"attestation_state":"computed","paper":{"title":"Proof of a conjecture on monomial graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Lazebnik, Stephen D. Lappano, Xiang-dong Hou","submitted_at":"2015-07-19T16:50:14Z","abstract_excerpt":"Let $e$ be a positive integer, $p$ be an odd prime, $q=p^{e}$, and $\\Bbb F_q$ be the finite field of $q$ elements. Let $f,g \\in \\Bbb F_q [X,Y]$. The graph $G=G_q(f,g)$ is a bipartite graph with vertex partitions $P=\\Bbb F_q^3$ and $L=\\Bbb F_q^3$, and edges defined as follows: a vertex $(p)=(p_1,p_2,p_3)\\in P$ is adjacent to a vertex $[l] = [l_1,l_2,l_3]\\in L$ if and only if $p_2 + l_2 = f(p_1,l_1)$ and $p_3 + l_3 = g(p_1,l_1)$. Motivated by some questions in finite geometry and extremal graph theory, Dmytrenko, Lazebnik and Williford conjectured in 2007 that if $f$ and $g$ are both monomials a"},"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":"1507.05306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-19T16:50:14Z","cross_cats_sorted":[],"title_canon_sha256":"ab84b2331f7043fae17713effc2bd9efa9dc565666ce0f2bc6a5b49ba7febcba","abstract_canon_sha256":"536c89d681be94a83b2d62b594343eecb87f17ea2b83f3488e791e010f0efd21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:37.243947Z","signature_b64":"Ft9PYjKFUFMj0yuWKzsfJR97W6/+jQYvVcaCu7wkCTY2tRHuVDLCQCpIc3Kac8czaouGaCGUt9ufoFfHDPysCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5a2080b06abaa4a856c4a50bf368ab1aa48851f6f4a87d86503d3f93b0a3d25","last_reissued_at":"2026-05-18T01:36:37.243202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:37.243202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of a conjecture on monomial graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Lazebnik, Stephen D. Lappano, Xiang-dong Hou","submitted_at":"2015-07-19T16:50:14Z","abstract_excerpt":"Let $e$ be a positive integer, $p$ be an odd prime, $q=p^{e}$, and $\\Bbb F_q$ be the finite field of $q$ elements. Let $f,g \\in \\Bbb F_q [X,Y]$. The graph $G=G_q(f,g)$ is a bipartite graph with vertex partitions $P=\\Bbb F_q^3$ and $L=\\Bbb F_q^3$, and edges defined as follows: a vertex $(p)=(p_1,p_2,p_3)\\in P$ is adjacent to a vertex $[l] = [l_1,l_2,l_3]\\in L$ if and only if $p_2 + l_2 = f(p_1,l_1)$ and $p_3 + l_3 = g(p_1,l_1)$. 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