Additive multiplicative increasing functions on nonnegative square matrices and multidigraphs

AbstractIt is known that if f is a multiplicative increasing function on N, then either f(n)=0 for all n∈N or f(n)=nα for some α⩾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