An introduction of F-graphs, a graph-theoretic representation of natural numbers
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 fami...
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171292000383 |
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| _version_ | 1832562438240731136 |
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| author | E. J. Farrell |
| author_facet | E. J. Farrell |
| author_sort | E. J. Farrell |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f861af6821ea444faf6f9b652c8f3b15 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f861af6821ea444faf6f9b652c8f3b152025-02-03T01:22:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115231331710.1155/S0161171292000383An introduction of F-graphs, a graph-theoretic representation of natural numbersE. J. Farrell0Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and TobagoA 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.http://dx.doi.org/10.1155/S0161171292000383cactus type graphscorepattern recognitionsemigroupsemigroup isomorphismnatural numbersancestor (graph)parent (graph)descendant (graph)F-graphattaching a graphbasis graphroot of an F-graph. |
| spellingShingle | E. J. Farrell An introduction of F-graphs, a graph-theoretic representation of natural numbers International Journal of Mathematics and Mathematical Sciences 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. |
| title | An introduction of F-graphs, a graph-theoretic representation of natural numbers |
| title_full | An introduction of F-graphs, a graph-theoretic representation of natural numbers |
| title_fullStr | An introduction of F-graphs, a graph-theoretic representation of natural numbers |
| title_full_unstemmed | An introduction of F-graphs, a graph-theoretic representation of natural numbers |
| title_short | An introduction of F-graphs, a graph-theoretic representation of natural numbers |
| title_sort | introduction of f graphs a graph theoretic representation of natural numbers |
| topic | 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. |
| url | http://dx.doi.org/10.1155/S0161171292000383 |
| work_keys_str_mv | AT ejfarrell anintroductionoffgraphsagraphtheoreticrepresentationofnaturalnumbers AT ejfarrell introductionoffgraphsagraphtheoreticrepresentationofnaturalnumbers |