Farrell, E. J. An introduction to \(F\)-graphs, a graph-theoretic representation of natural numbers. (English) Zbl 0753.05070 Int. J. Math. Math. Sci. 15, No. 2, 313-317 (1992). 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. Cited in 2 Documents MSC: 05C99 Graph theory 20M07 Varieties and pseudovarieties of semigroups Keywords:pattern recognition; semigroup isomorphism; attaching a graph; basis graph; family graphs; \(F\)-graphs; cactus-type graphs; commutative semigroup; representations of natural numbers PDFBibTeX XMLCite \textit{E. J. Farrell}, Int. J. Math. Math. Sci. 15, No. 2, 313--317 (1992; Zbl 0753.05070) Full Text: DOI EuDML