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

Yuji Hibino, Hun Hee Lee, Nobuaki Obata

研究成果: Article査読

1 被引用数 (Scopus)

抄録

Let G be a finite connected graph on two or more vertices, and G[N,k] the distance-k graph of the N-fold Cartesian power of G. For a fixed k ≥ 1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.

本文言語English
ページ(範囲)35-51
ページ数17
ジャーナルColloquium Mathematicum
132
1
DOI
出版ステータスPublished - 2013

ASJC Scopus subject areas

  • 数学 (全般)

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