{"paper":{"title":"On the signless Laplacian spectral radius of $K_{s,t}$-minor free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ming-Zhu Chen, Xiao-Dong Zhang","submitted_at":"2019-08-12T16:11:31Z","abstract_excerpt":"In this paper, we prove that if $G$ is a $K_{2,t}$-minor free graph of order $n\\geq t^2+4t+1$ with $t\\geq 3$, the signless Laplacian spectral radius $q(G)\\leq \\frac{1}{2}(n+2t-2+\\sqrt{(n-2t+2)^2+8t-8}\\ )$ with equality if and only if $n\\equiv 1~(\\mathrm{mod}~t)$ and $G=F_{2,t}(n)$, where $F_{s,t}(n):=K_{s-1}\\vee (p\\cdot K_t\\cup K_r)$ for $n-s+1=pt+r$ and $0\\leq r<t$. In particular, if $t=3$ and $n\\geq 22$, then $F_{2,3}(n)$ is the unique $K_{2,3}$-minor free graph of order $n$ with the maximum signless Laplacian spectral radius. In addition, $F_{3,3}(n)$ is the unique extremal graph with the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04221","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04221/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"}