Additive multiplicative increasing functions on nonnegative square matrices and multidigraphs

Abstract

It is known that if f is a multiplicative increasing function on N, then either f(n) = 0 for all n is an element of N or f (n) = n(alpha) for some alpha greater than or equal to 0. It is very natural to ask if there are similar results in other algebraic systems. In this paper, we first study the multiplicative increasing functions. over nonnegative square matrices with respect to tensor product and then restrict our result to multidigraphs and loopless multidigraphs. (C) 2001 Elsevier Science B.V. All rights reserved.