A Classification of Tightly Attached Half-Arc-Transitive Graphs of Valency 4
| dc.creator | Sparl, Primoz | |
| dc.date | 2006-06-29 | |
| dc.date.accessioned | 2026-07-07T07:17:51Z | |
| dc.date.available | 2026-07-07T07:17:51Z | |
| dc.description | A graph is said to be {\em half-arc-transitive} if its automorphism group acts transitively on the set of its vertices and edges but not on the set of its arcs. With each half-arc-transitive graph of valency 4 a collection of the so called {\em alternating cycles} is associated, all of which have the same even length. Half of this length is called the {\em radius} of the graph in question. Moreover, any two adjacent alternating cycles have the same number of common vertices. If this number, the so called {\em attachment number}, coincides with the radius, we say that the graph is {\em tightly attached}. In {\em J. Combin. Theory Ser. B} {73} (1998) 41--76, Marušič gave a classification of tightly attached \hatr graphs of valency 4 with odd radius. In this paper the even radius tightly attached graphs of valency 4 are classified, thus completing the classification of all tightly attached half-arc-transitive graphs of valency 4. | |
| dc.description | 36 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0606766 | |
| dc.identifier | http://arxiv.org/abs/math/0606766 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114094 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C25 | |
| dc.title | A Classification of Tightly Attached Half-Arc-Transitive Graphs of Valency 4 | |
| dc.type | text |