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 $1$.

Accepted: 2019-04-27

Revised after acceptance: 2019-05-29

Published online: 2019-12-04

DOI: https://doi.org/10.5802/alco.82

Classification: 05E18, 05C25, 20B25

Keywords: arc-transitive graph, edge-transitive graph, semi-symmetric graph, twin-free graph

@article{ALCO_2019__2_6_1275_0, author = {Conder, Marston D. E. and Verret, Gabriel}, title = {Edge-transitive graphs of small order and the answer to a 1967 question by Folkman}, journal = {Algebraic Combinatorics}, publisher = {MathOA foundation}, volume = {2}, number = {6}, year = {2019}, pages = {1275-1284}, doi = {10.5802/alco.82}, mrnumber = {4049846}, zbl = {1428.05326}, language = {en}, url = {alco.centre-mersenne.org/item/ALCO_2019__2_6_1275_0/} }

Conder, Marston D. E.; Verret, Gabriel. Edge-transitive graphs of small order and the answer to a 1967 question by Folkman. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1275-1284. doi : 10.5802/alco.82. https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1275_0/

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