ASYMPTOTIC SPECTRAL DISTRIBUTIONS OF DISTANCE-k GRAPHS OF CARTESIAN PRODUCT GRAPHS

作者：Hibino Yuji^*; Lee Hun Hee; Obata Nobuaki

来源：Colloquium Mathematicum, 2013, 132(1): 35-51.

DOI：10.4064/cm132-1-4

• adjacency matrix
• Cartesian product graph
• central limit theorem
• distance-k graph
• Hermite polynomials
• quantum probability
• spectrum

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 %26gt;= 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.

• 出版日期2013