{"paper":{"title":"On power graphs of finite groups with forbidden induced subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ahmad Erfanian, Alireza Doostabadi, Mohammad Farrokhi Derakhshandeh Ghouchan","submitted_at":"2014-01-27T07:22:14Z","abstract_excerpt":"The power graph $\\mathcal{P}(G)$ of a finite group $G$ is a graph whose vertex set is the group $G$ and distinct elements $x,y\\in G$ are adjacent if one is a power of the other, that is, $x$ and $y$ are adjacent if $x\\in\\langle y\\rangle$ or $y\\in\\langle x\\rangle$. We characterize all finite groups $G$ whose power graphs are claw-free, $K_{1,4}$-free or $C_4$-free."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6755","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"}