How to get the count of isomorphisms between two graphs?

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Suppose I have two weighted isomorphic graphs. How can I figure out how many isomorphisms between them there are?Please don't use "brute force" to do that.If it's too difficult,we can reduce the difficulty of the problem by change the question to how to figure out if there is only one isomorphism between these two graphs or not.Answer can be choosed from three options:have no isomorphism,only have one,have more than one.Thank you very much.