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

被引：2

作者：

Hibino, Yuji ^{[1
]}

Lee, Hun Hee ^{[2
,3
]}

Obata, Nobuaki ^{[4
]}

机构：

[1] Saga Univ, Dept Math, Saga 8408502, Japan

[2] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[3] Saga Univ, Res Inst Math, Saga 8408502, Japan

[4] Tohoku Univ, Grad Sch Informat Sci, Sendai, Miyagi 9808579, Japan

来源：

COLLOQUIUM MATHEMATICUM | 2013年 / 132卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

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

D O I：

10.4064/cm132-1-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：35 / 51

页数：17

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