{"paper":{"title":"Normal Subgroup Based Power Graph of a finite Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"A. K. Bhuniya, Sudip Bera","submitted_at":"2016-01-18T09:05:06Z","abstract_excerpt":"For a finite group $G$ with a normal subgroup $H$, the normal subgroup based power graph of $G$, denoted by $\\Gamma_H(G)$ whose vertex set $V(\\Gamma_H(G))=(G\\setminus H)\\bigcup \\{e\\}$ and two vertices $a$ and $b$ are edge connected if $aH=b^mH$ or $bH=a^nH$ for some $m, n \\in \\mathbb{N}$. In this paper we obtain some fundamental characterizations of the normal subgroup based power graph. We show some relation between the graph $\\Gamma_H(G)$ and the power graph $\\Gamma(\\frac{G}{H})$. We show that $\\Gamma_H(G)$ is complete if and only of $\\frac{G}{H}$ is cyclic group of order $1$ or $p^m$, where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04431","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"}