A First Look

Try moving the cursor over the five-sided graph!
The two versions of the same graph were created by moving only one vertex. Let's now take a look at another collection of graphs.

Variations of the Petersen Graph

These graphs may look different, but in fact they are different representations of the same graph, known as the Peterson Graph, named after the mathematician, Julius Petersen.  The five-sided graph is also a version of the Petersen Graph.  You can make any of the above graphs look like any other simply by moving vertices and edges into different positions.  You do not have to cut or add any vertices or edges in order to from change one graph to another.

Informally, two graphs are isomorphic if you can redraw one (by moving vertices, warping edges, or both) so that it is identical to the other.

Complete-4 isomorphic graphs

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