{"paper":{"title":"Connectivity of some Algebraically Defined 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":"2018-07-30T13:46:01Z","abstract_excerpt":"Let $p$ be a prime, $e$ a positive integer, $q = p^e$, and let $\\mathbb{F}_q$ denote the finite field of $q$ elements. Let $f_i : \\mathbb{F}_q^2\\to\\mathbb{F}_q$ be arbitrary functions, where $1\\le i\\le l$, $i$ and $l$ are integers. The digraph $D = D(q;\\bf{f})$, where ${\\bf f}=(f_1,\\dotso,f_l) : \\mathbb{F}_q^2\\to\\mathbb{F}_q^l$, is defined as follows. The vertex set of $D$ is $\\mathbb{F}_q^{l+1}$. There is an arc from a vertex ${\\bf x} = (x_1,\\dotso,x_{l+1})$ to a vertex ${\\bf y} = (y_1,\\dotso,y_{l+1})$ if $ x_i + y_i = f_{i-1}(x_1,y_1) $ for all $i$, $2\\le i \\le l+1$. In this paper we study t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11347","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}