Full friendly index sets of Cartesian products of two cycles

Let G = (V,E) be a connected simple graph. A labeling f: V . .2 induces an edge labeling f*: E . .2 defined by f*(xy) = f(x)+ f(y) for each xy . E. For i . .2, let . f (i) = |f .1(i)| and e f (i) = |f*.1(i)|. A labeling f is called friendly if |. f (1) . . f (0)| . 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by i f (G) = e f (1) . e f (0). The set {i f (G) | f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI(G). In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.