Signed 2-independence of Cartesian product of directed paths
Haichao Wang, Hye Kyung Kim · International Journal of Computer Mathematics · 2013
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 (S2IF) if f(N−[v])≤1 for every v in D. The weight of a S2IF is f(V(D))=∑v∈V(D)f(v). The maximum weight of a S2IF of D is the signed 2-independence number (or the lower against number) of D. Let Pm×Pn be the Cartesian product of directed paths Pm and Pn. In this paper, we determine the exact values of for 1≤m≤5 and n≥1.