Quote:

I interpret this as: For every v E V1 maps to a v E V2 + the ordered pairs (a, b) in E1 has an equivalent in E2 + the lables are preserved.

This is correct but not written completely precisely. Formally, this would be: There exists a bijection f: V1 -> V2 such that for every v1, v2 we have (v1, v2) in E1 iff (f(v1), f(v2)) in E2. There should be another condition for labels, but it is not clear from your description what the type of L1 and L2 is: are they sets? functions? I guess, usually labels are identified with nodes.