A Classification of Tightly Attached HalfArcTransitive Graphs of Valency 4
Abstract
A graph is said to be {\em halfarctransitive} if its automorphism group acts transitively on the set of its vertices and edges but not on the set of its arcs. With each halfarctransitive 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) 4176, 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 halfarctransitive graphs of valency 4.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606766
 Bibcode:
 2006math......6766S
 Keywords:

 Mathematics  Combinatorics;
 05C25
 EPrint:
 36 pages, 1 figure