{"paper":{"title":"The enhanced quotient graph of the quotient of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniel G. Mendoza, Luis A. Dupont, Miriam Rodr\\'iguez","submitted_at":"2017-07-04T18:29:10Z","abstract_excerpt":"For a finite group $G$ with a normal subgroup $H$, the enhanced quotient graph of $G/H$, denoted by $\\mathcal{G}_{H}(G),$ is the graph with vertex set $V=(G\\backslash H)\\cup \\{e\\}$ and two vertices $x$ and $y$ are edge connected if $xH = yH$ or $xH,yH\\in \\langle zH\\rangle$ for some $z\\in G$. In this article, we characterize the enhanced quotient graph of $G/H$. The graph $\\mathcal{G}_{H}(G)$ is complete if and only if $G/H$ is cyclic, and $\\mathcal{G}_{H}(G)$ is Eulerian if and only if $|G/H|$ is odd. We show some relation between the graph $\\mathcal{G}_{H}(G)$ and the enhanced power graph $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01127","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"}