{"paper":{"title":"Introduction to the McPherson number, $\\Upsilon(G)$ of a simple connected graph","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johan Kok, Susanth C","submitted_at":"2014-10-31T04:44:09Z","abstract_excerpt":"The concept of the \\emph{McPherson number} of a simple connected graph $G$ on $n$ vertices denoted by $\\Upsilon(G)$, is introduced. The recursive concept, called the \\emph{McPherson recursion}, is a series of \\emph{vertex explosions} such that on the first interation a vertex $v \\in V(G)$ explodes to arc (directed edges) to all vertices $u \\in V(G)$ for which the edge $vu \\notin E(G)$, to obtain the mixed graph $G'_1.$ Now $G'_1$ is considered on the second iteration and a vertex $w \\in V(G'_1) = V(G)$ may explode to arc to all vertices $z \\in V(G'_1)$ if edge $wz \\notin E(G)$ and arc $(w, z)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8637","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"}