{"paper":{"title":"A Study on Linear Jaco Graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johan Kok, Sunny Joseph Kalayathankal, Susanth C.","submitted_at":"2015-06-22T10:22:18Z","abstract_excerpt":"We introduce the concept of a family of finite directed graphs (\\emph{positive integer order,} $f(x) = mx + c; x,m \\in \\Bbb N$ and $c \\in \\Bbb N_0)$ which are directed graphs derived from an infinite directed graph called the $f(x)$-root digraph. The $f(x)$-root digraph has four fundamental properties which are; $V(J_\\infty(f(x))) = \\{v_i: i \\in \\Bbb N\\}$ and, if $v_j$ is the head of an arc then the tail is always a vertex $v_i, i < j$ and, if $v_k$ for smallest $k \\in \\Bbb N$ is a tail vertex then all vertices $v_\\ell, k < \\ell < j$ are tails of arcs to $v_j$ and finally, the degree of a vert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06538","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"}