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

Yuji Hibino, Hun Hee Lee, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)35-51
Number of pages17
JournalColloquium Mathematicum
Issue number1
Publication statusPublished - 2013


  • Adjacency matrix
  • Cartesian product graph
  • Central limit theorem
  • Distance-k graph
  • Hermite polynomials
  • Quantum probability
  • Spectrum

ASJC Scopus subject areas

  • Mathematics(all)


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