Daniel Pragel
Published 2011-10-16, updated 2013-05-11Version 2
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).
Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges
Nonpositive Eigenvalues of the Adjacency Matrix and Lower Bounds for Laplacian Eigenvalues
On bipartite cages of excess 4
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