# Asymptotic spectral analysis of growing graphs: odd graphs and spidernets

Daisuke Igarashi; Nobuaki Obata

Banach Center Publications (2006)

- Volume: 73, Issue: 1, page 245-265
- ISSN: 0137-6934

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topDaisuke Igarashi, and Nobuaki Obata. "Asymptotic spectral analysis of growing graphs: odd graphs and spidernets." Banach Center Publications 73.1 (2006): 245-265. <http://eudml.org/doc/282279>.

@article{DaisukeIgarashi2006,

abstract = {Two new examples are given for illustrating the method of quantum decomposition in the asymptotic spectral analysis for a growing family of graphs. The odd graphs form a growing family of distance-regular graphs and the two-sided Rayleigh distribution appears in the limit of vacuum spectral distribution of the adjacency matrix. For a spidernet as well as for a growing family of spidernets the vacuum distribution of the adjacency matrix is the free Meixner law. These distributions are calculated through the Jacobi parameters obtained from structural data of graphs.},

author = {Daisuke Igarashi, Nobuaki Obata},

journal = {Banach Center Publications},

keywords = {adjacency matrix; spectral distribution; quantum decomposition; Rayleigh distribution; free Meixner law; odd graph; spidernet; tree},

language = {eng},

number = {1},

pages = {245-265},

title = {Asymptotic spectral analysis of growing graphs: odd graphs and spidernets},

url = {http://eudml.org/doc/282279},

volume = {73},

year = {2006},

}

TY - JOUR

AU - Daisuke Igarashi

AU - Nobuaki Obata

TI - Asymptotic spectral analysis of growing graphs: odd graphs and spidernets

JO - Banach Center Publications

PY - 2006

VL - 73

IS - 1

SP - 245

EP - 265

AB - Two new examples are given for illustrating the method of quantum decomposition in the asymptotic spectral analysis for a growing family of graphs. The odd graphs form a growing family of distance-regular graphs and the two-sided Rayleigh distribution appears in the limit of vacuum spectral distribution of the adjacency matrix. For a spidernet as well as for a growing family of spidernets the vacuum distribution of the adjacency matrix is the free Meixner law. These distributions are calculated through the Jacobi parameters obtained from structural data of graphs.

LA - eng

KW - adjacency matrix; spectral distribution; quantum decomposition; Rayleigh distribution; free Meixner law; odd graph; spidernet; tree

UR - http://eudml.org/doc/282279

ER -

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