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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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