{"paper":{"title":"A note on solvable graphs of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Deiborlang Nongsiang, Parthajit Bhowal, Rajat Kanti Nath","submitted_at":"2019-03-05T10:14:16Z","abstract_excerpt":"Let $G$ be a finite non-solvable group with solvable radical $Sol(G)$. The solvable graph $\\Gamma_s(G)$ of $G$ is a graph with vertex set $G\\setminus Sol(G)$ and two distinct vertices $u$ and $v$ are adjacent if and only if $\\langle u, v \\rangle$ is solvable. We show that $\\Gamma_s (G)$ is not a star graph, a tree, an $n$-partite graph for any positive integer $n \\geq 2$ and not a regular graph for any non-solvable finite group $G$. We compute the girth of $\\Gamma_s (G)$ and derive a lower bound of the clique number of $\\Gamma_s (G)$. We prove the non-existence of finite non-solvable groups wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01755","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"}