Asymptotic spectral analysis of growing graphs: odd graphs and spidernets
Volume 73 / 2006
Banach Center Publications 73 (2006), 245-265
MSC: Primary 46L53; Secondary 05C50, 60F05, 81S25.
DOI: 10.4064/bc73-0-18
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.
