2017/09/26 by Hyunshik Shin, Shin, Hyunshik
Mathematics · #05C50 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50
paper · pdf · doi:10.48550/arxiv.1709.08871
5 pages
arxiv created 2017/09/26 · openalex publication_date 2017/09/26 · arxiv updated 2017/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ⋅ 1), that is, the starlike tree with k branches of length 1 and one branch of length n. The largest eigenvalue λ1 of S(n,k ⋅ 1) satisfies √(k+1) ≤ λ1 < k/√(k-1). Moreover, the largest eigenvalue of S(n,k ⋅ 1) is equal to the largest eigenvalue of S(k ⋅ (n+1) ), which is the starlike tree that has k branches of length n-1. Using the spectral radii of S(n,k ⋅ 1) we can show