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

Abstract

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.

Keywords

• cactus type graphs
• core
• pattern recognition
• semigroup
• semigroup isomorphism
• natural numbers
• ancestor (graph)
• parent (graph)
• descendant (graph)
• F-graph
• attaching a graph
• basis graph
• root of an F-graph.