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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?


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?

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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.

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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.

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