2006/06/29 by Primož Šparl, Primoz Sparl, Sparl, Primoz
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05C25
paper · pdf · doi:10.48550/arxiv.math/0606766
36 pages, 1 figure
arxiv created 2006/06/29 · arxiv updated 2009/12/01
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.