Determine whether the networks below are isomorphic

Question

Determine whether the networks below are isomorphic

They meet the requirements of both having the same number of vertices.

They have the same number of edges

They both have 8 vertices of degree 3.

Knowing that my knowledge tells me they are isomorphic.

But what's the best way to find out?

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EDIT;

matrix for both graphs:

   A B C D E F G H
A:   1       1   1
B: 1     1     1
C:         1 1   1   
D:   1     1 1
E:     1 1     1
F: 1   1 1          
G:   1     1     1
H: 1   1       1

   0 1 5 3 6 2 7 4
0:   1       1   1
1: 1     1     1
5:         1 1   1
3:   1     1 1
6:     1 1     1 
2: 1   1 1
7:   1     1     1
4: 1   1       1

Correct?

Answer 1

You might be able to find an isomorphism.
The symmetry of the network on the left helps. All vertices are equivalent.
For example:
* let $a$ correspond to $0$.
* the neighbours of $a$ are $b,f,h$. They would correspond to $1,2,4$ in some order. Again, by the symmetry of the left-hand network, it doesn't matter which order. Let $b=1$,$f=2$,$h=4$.
* $d$ is adjacent to $b$ and $f$, so $d=3$

And so on.

Answer 2

A square $a,f,d,b$ is in the graph with another square $h,c,e,g$ where the corresponding vertices of these squares are joined in the graph. This accounts for all the edges, making the graph that of a cube.