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

Yuji Hibino; Hun Hee Lee; Nobuaki Obata

Colloquium Mathematicae (2013)

- Volume: 132, Issue: 1, page 35-51
- ISSN: 0010-1354

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topYuji 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 -

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