Asymptotic spectral distributions of distance k-graphs of star product graphs

2014/08/25 by Octavio Arizmendi, Arizmendi, Octavio, Tulio Gaxiola +1 · 1 citation
Mathematics · #05C12 (Secondary) #05C50 (Primary) #47A10 #81S25 #FOS: Mathematics #Functional Analysis (math.FA) #Graph theory and applications #Limits and Structures in Graph Theory #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1408.5682

openalex publication_date 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite connected graph and let G^{[⋆ N,k]} be the distance k-graph of the N-fold star power of G. For a fixed k≥1, we show that the large N limit of the spectral distribution of G^{[⋆ N,k]} converges to a centered Bernoulli distribution, 1/2δ_-1+1/2δ₁. The proof is based in a fourth moment lemma for convergence to a centered Bernoulli distribution.

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