Constructing highly arc transitive digraphs using a layerwise direct product
Christoph Neumann
TL;DR
This paper presents a new method for constructing highly arc transitive digraphs using a layerwise direct product, enabling the creation of new examples and counterexamples to existing conjectures in the field.
Contribution
The paper introduces a generalized construction technique for highly arc transitive digraphs that extends known classes and provides counterexamples to a conjecture by Cameron, Praeger, and Wormald.
Findings
The layerwise direct product generalizes existing classes of highly arc transitive digraphs.
New examples of highly arc transitive digraphs are constructed.
Counterexamples to a conjecture on the structure of such digraphs are provided.
Abstract
We introduce a construction of highly arc transitive digraphs using a layerwise direct product. This product generalizes some known classes of highly arc transitive digraphs but also allows to construct new such. We use the product to obtain counterexamples to a conjecture by Cameron, Praeger and Wormald on the structure of certain highly arc transitive digraphs.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Graph Theory Research · graph theory and CDMA systems