Determinants of Box Products of Paths
Combinatorics
2013-05-14 v2
Abstract
Suppose that G is the graph obtained by taking the box product of a path of length n and a path of length m. Let M be the adjacency matrix of G. If n=m, H.M. Rara showed in 1996 that det(M)=0. We extend this result to allow n and m to be any positive integers, and show that, if gcd(n+1,m+1)>1, then det(M)=0; otherwise, if gcd(n+1,m+1)=1, then det(M)=(-1)^(nm/2).
Cite
@article{arxiv.1110.3497,
title = {Determinants of Box Products of Paths},
author = {Daniel Pragel},
journal= {arXiv preprint arXiv:1110.3497},
year = {2013}
}