Integer invariants of abelian Cayley graphs
Combinatorics
2013-12-13 v2 Spectral Theory
Abstract
Let be a finite abelian group, let be a subset of , and form the Cayley (directed) graph of with connecting set . We explain how, for various matrices associated to this graph, the spectrum can be used to give information on the Smith normal form. This technique is applied to several interesting examples, including matrices in the Bose-Mesner algebra of the Hamming association scheme . We also recover results of Bai and Jacobson-Niedermaier-Reiner on the critical group of a Cartesian product of complete graphs.
Cite
@article{arxiv.1308.2335,
title = {Integer invariants of abelian Cayley graphs},
author = {Joshua E. Ducey and Deelan M. Jalil},
journal= {arXiv preprint arXiv:1308.2335},
year = {2013}
}
Comments
8 pages. Many small changes, mostly to make references more precise and to explain notation and terminology. The biggest changes are to Section 3, where we are now more careful with the statements of the theorems and their proofs