The problem of singularity for planar grids

Abstract: We consider simple graphs and their adjacency matrices. In , Rara (1996) gives methods of reducing graphs which simplify the procedure of computing the determinant of their adjacency matrices. We continue this subject matter and give a general method of reducing graphs. By the use of this method we define a formula for computing the determinant of any planar grid and in particular settle the problem of their singularity. [Copyright &y& Elsevier]