What are the steps to use Nauty and Traces for determining whether two graphs are isomorphic?

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Install Nauty and Traces: Nauty and Traces are open-source software packages that allow you to determine whether two graphs are isomorphic. You can download them from the official website: http://pallini.di.uniroma1.it/.

Input the two graphs: The first step is to input the two graphs that you want to check for isomorphism. You can either input the graph as an adjacency matrix or as a list of edges.

Run the nauty program: Once you have inputted the two graphs, you need to run the nauty program. This program will generate a canonical form for each graph, which you can use to compare the two graphs.

Compare the canonical forms: After generating the canonical forms, you need to compare them to determine whether the two graphs are isomorphic. If the two canonical forms match, then the graphs are isomorphic. If the canonical forms do not match, then the two graphs are not isomorphic.

Interpret the results: Finally, you need to interpret the results. If the two graphs are isomorphic, you can use the canonical form to find a mapping between the vertices of the two graphs. If the two graphs are not isomorphic, you can identify the differences between the two graphs.