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New structural results on tetravalent half-arc-transitive graphs
Ramos Rivera, Alejandra (Author), Šparl, Primož (Author)

URLURL - Presentation file, Visit https://doi.org/10.1016/j.jctb.2018.08.006 This link opens in a new window

Abstract
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.

Language:English
Keywords:half-arc-transitive, tetravalent, alternating cycle, alternating jump, quotient graph
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Year:2019
Number of pages:Str. 256-278
Numbering:Vol. 135
UDC:519.17
ISSN on article:0095-8956
DOI:10.1016/j.jctb.2018.08.006 This link opens in a new window
COBISS.SI-ID:1540554436 This link opens in a new window
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Downloads:32
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Record is a part of a journal

Title:Journal of combinatorial theory
Shortened title:J. comb. theory, Ser. B
Publisher:Academic Press
ISSN:0095-8956
COBISS.SI-ID:25721600 This link opens in a new window

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