{"paper":{"title":"Competition Graphs of Jaco Graphs and the Introduction of the Grog Number of a Simple Connected Graph","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":"2015-02-06T08:29:19Z","abstract_excerpt":"Let $G^\\rightarrow$ be a simple connected directed graph on $n \\geq 2$ vertices and let $V^*$ be a non-empty subset of $V(G^\\rightarrow)$ and denote the undirected subgraph induced by $V^*$ by, $\\langle V^* \\rangle.$ We show that the \\emph{competition graph} of the Jaco graph $J_n(1), n \\in \\Bbb N, n \\geq 5,$ denoted by $C(J_n(1))$ is given by:\\\\ \\\\ $C(J_n(1)) = \\langle V^* \\rangle_{V^* = \\{v_i|3 \\leq i \\leq n-1\\}} - \\{v_iv_{m_i}| m_i = i + d^+_{J_n(1)}(v_i), 3 \\leq i \\leq n-2\\} \\cup \\{v_1, v_2, v_n\\}.$\\\\ \\\\ Further to the above, the concept of the \\emph{grog number} $g(G^\\rightarrow)$ of a si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01824","kind":"arxiv","version":2},"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"}