Kronecker Product Graphs and Counting Walks in Restricted Lattices

Abstract

Formulas are derived for counting walks in the Kronecker product of graphs, and the associated spectral distributions are obtained by the Mellin convolution of probability distributions. Two-dimensional restricted lattices admitting the Kronecker product structure are listed, and their spectral distributions are calculated in terms of elliptic integrals.

14 pages, 6 figures