Isomorphism between graphs with coloured edges

Question

I have two graphs with verteces numbered from $1$ to $7$ and coloured edges. When can I say that these two graphs are not isomorphic? Can someone give me the definition?

Thanks!

Answer 1

In graph theory, an isomorphism of graphs $G$ and $H$ is a bijection between the vertex sets of $G$ and $H$

$f : V(G) \to V(H) $

such that any two vertices $u$ and $v$ of $G$ are adjacent in $G$ if and only if $f(u)$ and $f(v)$ are adjacent in $H$.

So you permute the vertices according to the isomorphism. So suppose edge between $1$ and $3$(if there is one) is of red colour, and $f(1)$ and $f(3)$ had edge of blue colour, then obviously it is not an isomorphism. Just rely on the definition, colouring or not.