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1.
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 birthday
Primož 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: 792; Downloads: 16
.pdf Full text (370,47 KB)

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A finite simple group is CCA if and only if it has no element of order four
Luke Morgan, Joy Morris, Gabriel Verret, 2020, original scientific article

Keywords: CCA problem, Cayley graphs, edge-colouring
Published in RUP: 02.12.2020; Views: 1010; Downloads: 34
URL Link to full text

4.
Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups
Luke Morgan, Joy Morris, Gabriel Verret, 2020, original scientific article

Keywords: Cayley digraphs, Cayley index
Published in RUP: 17.06.2020; Views: 1544; Downloads: 38
.pdf Full text (396,72 KB)

5.
Arc-transitive digraphs of given out-valency and with blocks of given size
Luke Morgan, Primož Potočnik, Gabriel Verret, 2019, original scientific article

Abstract: Given integers ▫$k$▫ and ▫$m$▫, we construct a ▫$G$▫-arc-transitive graph of valency ▫$k$▫ and an ▫$L$▫-arc-transitive oriented digraph of out-valency ▫$k$▫ such that ▫$G$▫ and ▫$L$▫ both admit blocks of imprimitivity of size ▫$m$▫.
Keywords: arc-transitive digraphs, Cayley digraphs, imprimitive digraphs
Published in RUP: 28.06.2019; Views: 1557; Downloads: 126
URL Link to full text

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7.
Cayley graphs on abelian groups
Edward Dobson, Pablo Spiga, Gabriel Verret, 2015, original scientific article

Keywords: Cayley graph, abelian group, automorphism
Published in RUP: 03.04.2017; Views: 2250; Downloads: 136
URL Link to full text

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On the order of arc-stabilizers in arc-transitive graphs
Gabriel Verret, 2009, published scientific conference contribution abstract

Keywords: arc-transitivie graph, arc-stabilizer, automorphism group
Published in RUP: 15.10.2013; Views: 3083; Downloads: 70
URL Link to full text

10.
Shifts in Cayley graphs
Gabriel Verret, Boštjan Brešar, 2007, published scientific conference contribution abstract

Keywords: teorija grafov, presečni grafi, medianski grafi
Published in RUP: 15.10.2013; Views: 4032; Downloads: 46
URL Link to full text

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