Transfinite Digraphs
| dc.creator | Zemanian, A. H. | |
| dc.date | 2009-04-27 | |
| dc.date.accessioned | 2026-07-07T13:08:58Z | |
| dc.date.available | 2026-07-07T13:08:58Z | |
| dc.description | Transfinite graphs have been defined and examined in a variety of prior works, but transfinite digraphs had not as yet been investigated. The present work embarks upon such a task. As with the ordinals, transfinite digraphs appear in a hierarchy of ranks indexed by the countable ordinals. The digraphs of rank 0 are the conventional digraphs. Those of rank 1 are constructed by defining certain extremities of 0-ranked digraphs, and then partitioning those extremities to obtain vertices of rank 1. Then, digraphs of rank 0 are connected together at those vertices of rank 1 to obtain a digraph of rank 1. This process can be continued through the natural-number ranks. However, to achieve a digraph whose rank is the first infinite ordinal $ω$ (i.e., the first limit ordinal), a special kind of transfinite digraph, which we call a digraph with an "arrow rank" must first be constructed in a way different from those of natural-number rank. Then, digraphs of still higher ranks can be constructed in a way similar to that for the natural-number ranked digraphs. However, just before each limit-ordinal rank, a digraph of arrow rank must be set up. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0904.4162 | |
| dc.identifier | http://arxiv.org/abs/0904.4162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228592 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C99 | |
| dc.title | Transfinite Digraphs | |
| dc.type | text |