## An introduction to $$F$$-graphs, a graph-theoretic representation of natural numbers.(English)Zbl 0753.05070

Summary: 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.

### MSC:

 05C99 Graph theory 20M07 Varieties and pseudovarieties of semigroups
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