Article ID Journal Published Year Pages File Type
4648116 Discrete Mathematics 2012 4 Pages PDF
Abstract

Suppose that GG is the graph obtained by taking the box product of a path of length nn and a path of length mm. Let M be the adjacency matrix of GG. In 1996, Rara showed that, if n=mn=m, then det(M)=0. We extend this result to allow nn and mm to be any positive integers, and show that det(M)={0if gcd(n+1,m+1)≠1,(−1)nm/2if gcd(n+1,m+1)=1.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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