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

Yuji Hibino, Hun Hee Lee, and Nobuaki Obata. "Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs." Colloquium Mathematicae 132.1 (2013): 35-51. <http://eudml.org/doc/283882>.

@article{YujiHibino2013,
abstract = {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.},
author = {Yuji Hibino, Hun Hee Lee, Nobuaki Obata},
journal = {Colloquium Mathematicae},
keywords = {adjacency matrix; Cartesian product graph; central limit theorem; distance-k graph; Hermite polynomials; quantum probability; spectrum},
language = {eng},
number = {1},
pages = {35-51},
title = {Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs},
url = {http://eudml.org/doc/283882},
volume = {132},
year = {2013},
}

TY - JOUR
AU - Yuji Hibino
AU - Hun Hee Lee
AU - Nobuaki Obata
TI - Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs
JO - Colloquium Mathematicae
PY - 2013
VL - 132
IS - 1
SP - 35
EP - 51
AB - 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.
LA - eng
KW - adjacency matrix; Cartesian product graph; central limit theorem; distance-k graph; Hermite polynomials; quantum probability; spectrum
UR - http://eudml.org/doc/283882
ER -