I am home studying graph theory

I have a definition of Isomorphism as follows.

G1 = (v1, E1, L1)

G2 = (V2, E2, L2)

G1 is isomorphic to G2 if

1: there is a bijective mapping between V1 and V2

2: edges between pairs of verticies in G1 must present between the corresponding pair of verties in G2

3: the lables are preserved by condition 1

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.

1: Is that about right?

2: bijective mapping in general is: f(a) = b - such that 1 element of 'a' maps to one element of 'b' - in graph theory do you need a function of is it just a case of searching the graph and chacking the mapping is correct?

Regards

Richard.