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

Abstract

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∼[v]) ≤ 1 for every v in D. The weight of a signed 2-independence function is f(V(D)) = Σ_v∈v(D)f(v). The maximum weight of a signed 2-independence function of D is the signed 2-independence number α²_s(D) of D. Let C_m × 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 α²_s(C_m × P_n) when 2 ≤ m ≤ 5 and n≥ 1.