Signed 2-independence of Cartesian product of directed cycles and paths

A two-valued function f : V (D) -> {-1,1} defined on the vertices of a digraph D = (V (D), A(D)) is called a signed 2-independence function if f (N- [nu]) <= 1 for every nu in D. The weight of a signed 2-independence function is f (V (D)) = Sigma(nu is an element of V(D)) f (nu). The maximum weight of a signed 2-independence function of D is the signed 2-independence number alpha(2)(s)(D) of D. Let C-m x P-n, be the Cartesian product of directed cycle C-m and directed path P-n. In this paper, we determine the exact values of alpha(2)(s) (C-m x P-n) when 2 <= m <= 5 and n >= 1.