An introduction of F-graphs, a graph-theoretic representation of natural numbers

A special type of family graphs (F-graphs, for brevity) are introduced. These are cactus-type graphs which form infinite families under an attachment operation. Some of the characterizing properties of F-graphs are discussed. Also, it is shown that, together with the attachment operation, these families form an infinite, commutative semigroup with unit element. Finally, it is shown that F-graphs are graph-theoretical representations of natural numbers