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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-18,
author = {Daisuke Igarashi and Nobuaki Obata},
title = {Asymptotic spectral analysis of growing graphs: odd graphs and spidernets},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {245-265},
zbl = {1109.46055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-18}
}
Daisuke Igarashi; Nobuaki Obata. Asymptotic spectral analysis of growing graphs: odd graphs and spidernets. Banach Center Publications, Tome 72 (2006) pp. 245-265. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-18/