{"paper":{"title":"Diameter of Cayley graphs of permutation groups generated by transposition trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Ashwin Ganesan","submitted_at":"2011-11-14T07:07:51Z","abstract_excerpt":"Let $\\Gamma$ be a Cayley graph of the permutation group generated by a transposition tree $T$ on $n$ vertices. In an oft-cited paper \\cite{Akers:Krishnamurthy:1989} (see also \\cite{Hahn:Sabidussi:1997}), it is shown that the diameter of the Cayley graph $\\Gamma$ is bounded as $$\\diam(\\Gamma) \\le \\max_{\\pi \\in S_n}{c(\\pi)-n+\\sum_{i=1}^n \\dist_T(i,\\pi(i))},$$ where the maximization is over all permutations $\\pi$, $c(\\pi)$ denotes the number of cycles in $\\pi$, and $\\dist_T$ is the distance function in $T$. In this work, we first assess the performance (the sharpness and strictness) of this upper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3114","kind":"arxiv","version":3},"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"}