As I said, I am working on isomorph-free exhaustive generation of graphs.
So far I have explained what does graph isomorphism and graph generation means. Isomorph-free exhaustive generation of a family graphs means generating that family of graphs in a way that
none of the two generated graphs are isomorphic to each other. The importance of isomorph-free generation is that as a model there is no difference
between two isomorph graphs so having isomorph graphs is redundant and also generally a graph, specially the big ones, can have exponentially so many isomorph versions (even with a fixed set of possible labels).
So practically having so many redundant data can make the generation algorithm useless.
Moreover, I should note that the term exhaustive means that the method generates whole the family because there are many researches in which some graphs
in a family are generated instead of the whole family.