New structural results on tetravalent half-arc-transitive graphs
Tetravalent graphs admitting a half-arc-transitive subgroup of automorphisms, that is a subgroup acting transitively on its vertices and its edges but not on its arcs, are investigated. One of the most fruitful approaches for the study of structural properties of such graphs is the well known paradigm of alternating cycles and their intersections which was introduced by Marušič 20 years ago. In this paper a new parameter for such graphs, giving a further insight into their structure, is introduced. Various properties of this parameter are given and the parameter is completely determined for the tightly attached examples in which any two non-disjoint alternating cycles meet in half of their vertices. Moreover, the obtained results are used to establish a link between two frameworks for a possible classification of all tetravalent graphs admitting a half-arc-transitive subgroup of automorphisms, the one proposed by Marušič and Praeger in 1999, and the much more recent one proposed by Al-bar, Al-kenai, Muthana, Praeger and Spiga which is based on the normal quotients method. New results on the graph of alternating cycles of a tetravalent graph admitting a half-arc-transitive subgroup of automorphisms are obtained. A considerable step towards the complete answer to the question of whether the attachment number necessarily divides the radius in tetravalent half-arc-transitive graphs is made.
2019
2021-04-07 05:06:21
1033
half-arc-transitive, tetravalent, alternating cycle, alternating jump, quotient graph,
dk_c
Alejandra
Ramos Rivera
70
Primož
Šparl
70
UDK
4
519.17
ISSN pri članku
9
0095-8956
DOI
15
10.1016/j.jctb.2018.08.006
COBISS_ID
3
1540554436
OceCobissID
13
25721600
0
Predstavitvena datoteka
2021-04-07 05:06:23