The friendly index set of Pm × Pn - Salehi, Ebrahim; Bayot, Denrick (Utilitas Mathematica, 2010)
For a graph G = (V, E) and a binary labeling (coloring) f : V(G) → Z2, let vf(i) = |f-1(i)| f is said to be friendly if |vf(1) - vf(0)| ≤ 1. The labeling f : V(G) → Z2 induces an edge labeling f* : E(G) → Z2 defined by f*(xy) = |f(x) - f(y)| ∀ xy € E(G). Let e f,(i) = |f*-1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef(1) - e f(0)| : f is a friendly vertx labeling of G }. In this paper we determine the friendly index set of Pm × Pn.