There are several free ‘graph theory programs’ available on the web.
Several of these the capacity to compare two graphs for an isomorphic relation. Basically they are programmed to compare the two adjacency matrices to see if one matrix can be transform by elementary operations into the other matrix. (That programming if beyond me of course.)
There is a simple way to see that two graphs are not isomorphic: If they have different degree sequences. Now they can have the same degree sequence and still not be isomorphic. That is, it is necessary that two graphs have the same degree sequence in order to be isomorphic, but it is not sufficient