Geodesic
Edge-transitive graphs of small order and the answer to a 1967 question by Folkman
Conder, Marston D. E.1 ; Verret, Gabriel1
1 Department of Mathematics University of Auckland Private Bag 92019 Auckland 1142 New Zealand
Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1275-1284 Cet article a éte moissonné depuis la source Numdam

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In this paper, we introduce a method for finding all edge-transitive graphs of small order, using faithful representations of transitive permutation groups of small degree, and we explain how we used this method to find all edge-transitive graphs of order up to 47, and all bipartite edge-transitive graphs of order up to 63. We also give an answer to a 1967 question of Folkman about semi-symmetric graphs of large valency; in fact we show that for semi-symmetric graphs of order 2n and valency d, the ratio d/n can be arbitrarily close to 1.

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DOI : 10.5802/alco.82
Classification : 05E18, 05C25, 20B25
Keywords: arc-transitive graph, edge-transitive graph, semi-symmetric graph, twin-free graph

Conder, Marston D. E. 1 ; Verret, Gabriel 1

1 Department of Mathematics University of Auckland Private Bag 92019 Auckland 1142 New Zealand
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Conder, Marston D. E.; Verret, Gabriel. Edge-transitive graphs of small order and the answer to a 1967 question by Folkman. Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1275-1284. doi: 10.5802/alco.82

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