{"paper":{"title":"The largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cunxiang Duan, Ligong Wang, Peng Xiao","submitted_at":"2018-07-16T16:25:52Z","abstract_excerpt":"Let $S_{1}(m, d, k)$ be the $k$-uniform supertree obtained from a loose path $P:v_{1}, e_{1}, v_{2}, \\ldots,v_{d}, e_{d}, v_{d+1}$ with length $d$ by attaching $m-d$ edges at vertex $v_{\\lfloor\\frac{d}{2}\\rfloor+1}.$ Let $\\mathbb{S}(m,d,k)$ be the set of $k$-uniform supertrees with $m$ edges and diameter $d$ and $q(G)$ be the signless Laplacian spectral radius of a $k$-uniform hypergraph $G$. In this paper, we mainly determine $S_{1}(m,d,k)$ with the largest signless Laplacian spectral radius among all supertrees in $\\mathbb{S}(m,d,k)$ for $3\\leq d\\leq m-1$. Furthermore, we determine the uniqu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05955","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":""},"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"}