Some recent discoveries about half-arc-transitive graphs
Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 149-162.

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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.
DOI : 10.26493/1855-3974.557.b5f
Mots-clés : Graph, edge-transitive, vertex-transitive, half-arc-transitive. 
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Marston D. E. Conder; Primož Potočnik; Primož Šparl. Some recent discoveries about half-arc-transitive graphs. Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 149-162. doi : 10.26493/1855-3974.557.b5f. https://geodesic-test.mathdoc.fr/articles/10.26493/1855-3974.557.b5f/

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