1. Basic tetravalent oriented graphs of independent-cycle typeNemanja Poznanović, Cheryl E. Praeger, 2025, original scientific article Abstract: The family OG(4) consisting of graph-group pairs (Γ, G), where Γ is a finite, connected, 4-valent graph admitting a G-vertex-, and G-edge-transitive, but not G-arc-transitive action, has recently been examined using a normal quotient methodology. A subfamily of OG(4) has been identified as ‘basic’, due to the fact that all members of OG(4) are normal covers of at least one basic pair. We provide an explicit classification of those basic pairs (Γ, G) which have at least two independent cyclic G-normal quotients (these are G-normal quotients which are not extendable to a common cyclic normal quotient).
Keywords: half-arc-transitive, vertex-transitive graph, edge-transitive graph, normal cover, cycle graph
Published in RUP: 21.10.2025; Views: 398; Downloads: 1
 Full text (398,19 KB) |
2. Some recent discoveries about half-arc-transitive graphs : dedicated to Dragan Marušič on the occasion of his 60th birthdayMarston D. E. Conder, Primož Potočnik, Primož Šparl, 2015, original scientific article 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 ▫$D_4$▫ (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: graph, edge-transitive, vertex-transitive, arc-transitive, half arc-transitive
Published in RUP: 31.12.2021; Views: 2645; Downloads: 24
Full text (333,06 KB) |
3. A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two : dedicated to Dragan Marušič on the occasion of his 60th birthdayPrimož Potočnik, Pablo Spiga, Gabriel Verret, 2015, original scientific article Abstract: A complete list of all connected arc-transitive asymmetric digraphs of in-valence and out-valence 2 on up to 1000 vertices is presented. As a byproduct, a complete list of all connected 4-valent graphs admitting a half-arc-transitive group of automorphisms on up to 1000 vertices is obtained. Several graph-theoretical properties of the elements of our census are calculated and discussed.
Keywords: graphs, digraphs, edge-transitive, vertex-transitive, arc-transitive, half arc-transitive
Published in RUP: 31.12.2021; Views: 2432; Downloads: 19
Full text (370,47 KB) |
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