  We propose a partitioning of the set of unlabelled, connected cubic graphs
into two disjoint subsets named genes and descendants, where the cardinality of
the descendants is much larger than that of the genes. The key distinction
between the two subsets is the presence of special edge cut sets, called
crackers, in the descendants. We show that every descendant can be created by
starting from a finite set of genes, and introducing the required crackers by
special breeding operations. We prove that it is always possible to identify
genes that can be used to generate any given descendant, and provide inverse
operations that enable their reconstruction. A number of interesting properties
of genes may be inherited by the descendant, and we therefore propose a natural
algorithm that decomposes a descendant into its ancestor genes. We conjecture
that each descendant can only be generated by starting with a unique set of
ancestor genes. The latter is supported by numerical experiments.
