{"paper":{"title":"Groups with maximum vertex degree commuting graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"G. Arunkumar, Sushil Bhunia","submitted_at":"2019-08-22T07:07:34Z","abstract_excerpt":"Let $G$ be a group and $Z(G)$ be its center. We associate a commuting graph ${\\Gamma}(G)$, whose vertex set is $G\\setminus Z(G)$ and two distinct vertices are adjacent if they commute. We say that ${\\Gamma}(G)$ is strong $k$ star free if the $k$ star graph is not a subgraph of ${\\Gamma}(G)$. In this paper, we characterize all strong $5$ star free commuting graphs. As a byproduct, we classify all strong claw-free graphs. Also, we prove that the set of all non-abelian groups whose commuting graph is strong $k$ star free is finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08226","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08226/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}