I have an assignment that state as following:

Let S be an amount (not empty) and designate with F 2 ^ (S Z), the amount of all relations G between S and Z, which is a graph (Z = integers).

(a)

Define a relation to F, with the property that a graph G_1 is in relation to graph G_2, if and only if: g_1 (s) g_2 (s) for all s S. Here, g_j is the function of the graph G_j, for j = 1.2. 

I got no idea how to make this assignment. Would appreciate any help.

What does it mean that a graph G_1 is in relation to another graph G_2?