{"paper":{"title":"Spectral radius of a star with one long arm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hyunshik Shin","submitted_at":"2017-09-26T07:56:04Z","abstract_excerpt":"A tree is said to be starlike if exactly one vertex has degree greater than two. In this paper, we will study the spectral properties of $S(n,k \\cdot 1)$, that is, the starlike tree with $k$ branches of length 1 and one branch of length $n$. The largest eigenvalue $\\lambda_1$ of $S(n,k \\cdot 1)$ satisfies $\\sqrt{k+1} \\leq \\lambda_1 < k/\\sqrt{k-1}$. Moreover, the largest eigenvalue of $S(n,k \\cdot 1)$ is equal to the largest eigenvalue of $S(k \\cdot (n+1) )$, which is the starlike tree that has $k$ branches of length $n-1$. Using the spectral radii of $S(n,k \\cdot 1)$ we can show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08871","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"}