how to determine if two graphs are not isomorphic What are some good ways of determining if two reasonably simple looking graphs are not isomorphic? I know that you can check their cycle or some weird property (for certain graphs), but are there some other tricks to do this?

Use a computer. "Nauty and Trace" programs gives a computational procedure to solve this problem. This open source package is available from http://pallini.di.uniroma1.it/.
Another helpful link may be
http://www.dharwadker.org/tevet/isomorphism/
