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arXiv · 1110.3497

Determinants of Box Products of Paths

Daniel Pragel
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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).

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Daniel Pragel. 2013-05-11. Determinants of Box Products of Paths. https://doi.org/10.1016/j.disc.2012.01.038

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