Some recent discoveries about half-arc-transitive graphs - Conder, Marston D. E. (Ars mathematica contemporanea, 2015)
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 ?$D_4$? (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.
Keywords: arc-transitive; edge-transitive; graf; graph; half arc-transitive; pol-ločno-tranzitiven; povezavno-tranzitiven; vertex-transitive; vozliščno-tranzitiven