Some recent discoveries about half-arc-transitive graphs

Authors

  • Marston D. E. Conder University of Auckland
  • Primož Potočnik University of Ljubljana
  • Primož Šparl University of Ljubljana

DOI:

https://doi.org/10.26493/1855-3974.557.b5f

Keywords:

Graph, edge-transitive, vertex-transitive, half-arc-transitive.

Abstract

We present some new discoveries about graphs that are half-arc-transitive (that is, vertex- and edge-transitive but not arc-transitive). These include the recent discovery of the smallest half-arc-transitive 4-valent graph with vertex-stabiliser of order 4, and the smallest with vertex-stabiliser of order 8, two new half-arc-transitive 4-valent graphs with dihedral vertex-stabiliser D4 (of order 8), and the first known half-arc-transitive 4-valent graph with vertex-stabiliser of order 16 that is neither abelian nor dihedral. We also use half-arc-transitive group actions to provide an answer to a recent question of Delorme about 2-arc-transitive digraphs that are not isomorphic to their reverse.

Published

2014-09-19

Issue

Section

Special Issue in Honor of the 60th Birthday of Professor Dragan Marušič