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.
ASJC Scopus subject areas
- 数学 (全般)