Let G be a finite connected graph on two or more vertices, and 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 . The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-4,
author = {Yuji Hibino and Hun Hee Lee and Nobuaki Obata},
title = {Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {35-51},
zbl = {1275.05034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-4}
}
Yuji Hibino; Hun Hee Lee; Nobuaki Obata. Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs. Colloquium Mathematicae, Tome 131 (2013) pp. 35-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-4/