International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 313-317
An introduction of -graphs, a graph-theoretic representation of natural numbers
Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and Tobago
Received 4 April 1987; Revised 26 June 1990
Copyright © 1992 E. J. Farrell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A special type of family graphs (-graphs, for brevity) are introduced. These are cactus-type graphs which form infinite families under an attachment operation. Some of the characterizing properties of -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 -graphs are graph-theoretical representations of natural numbers.