Generating algebraic expressions for labeled grid graphs

Abstract

The paper investigates relationship between algebraic expressions and labeled graphs. We consider directed grid graphs having m rows and n columns. Our intent is to simplify the expressions of these graphs. With that end in view, we describe two methods which generate expressions for directed grid graphs. For both methods, lengths of the expressions grow polynomially with n while m is determined as a constant parameter. Besides, we apply these methods to a square grid graph in which the number of rows is equal to the number of columns. We prove that the lengths of the expressions derived by the methods depend exponentially and quasi-polynomially, respectively, on the size of the graph.