Re: Need Graph Isomorphism Algorithm De-bunked

fgrieu wrote:
Mike Amling wrote:
....
An alternative to step 6 is to output the graph in generic
order based on a sort of the results, making a much shorter
and useful representative of the graph's equivalence class
(this has been suggested by Bill Cox).
I however fail to convince myself that this is equivalent;
or that the "compare graph's hash" variant never falsely
declare graphs isomorphic, or that the "compare sorted
graphs" variant never falsely declare graphs non-isomorphic.

François Grieu

I think it is sufficient to represent the graph over the equivalence
class of its vertices. Let N be the number of equivalence classes over
the vertices in the graph. Let A be a modified N*N adjacency matrix
such that A[i,j] is the number of edges from vertices in equivalence
class i to vertices in equivalence class j. To handle vertices with
zero degree the original number of vertices will have to be output as
well.

I don't know much graph theory, so I apologize if this representation
already has a name or a better description, or if it doesn't actually
work.

Ben Livengood

.

Relevant Pages

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