Sharply $k$-arc-transitive-digraphs: finite and infinite examples
R\"ognvaldur G. M\"oller (1), Primo\v{z} Poto\v{c}nik (2), Norbert, Seifter (3) ((1) University of Iceland, Reykjav\'ik, Iceland, (2) University, of Ljubljana, Ljubljana, Slovenia, (3) Montanuniversit\"at Leoben, Austria)
TL;DR
This paper introduces a general method for constructing both finite and infinite sharply $k$-arc-transitive digraphs, expanding the known examples and including those with polynomial growth and varying ends.
Contribution
A novel construction method for sharply $k$-arc-transitive digraphs, applicable to finite and infinite cases with diverse structural properties.
Findings
Constructed new finite sharply $k$-arc-transitive digraphs.
Produced infinite examples with different numbers of ends.
Included examples with polynomial growth.
Abstract
A general method for constructing sharply -arc-transitive digraphs, i.e. digraphs that are -arc-transitive but not -arc-transitive, is presented. Using our method it is possible to construct both finite and infinite examples. The infinite examples can have one, two or infinitely many ends. Among the one-ended examples there are also digraphs that have polynomial growth.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Graph Theory Research · semigroups and automata theory