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:

Revised after acceptance:

Published online:

DOI: 10.5802/alco.82

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

^{1}; Verret, Gabriel

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@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}, pages = {1275--1284}, publisher = {MathOA foundation}, volume = {2}, number = {6}, year = {2019}, doi = {10.5802/alco.82}, mrnumber = {4049846}, zbl = {1428.05326}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.82/} }

TY - JOUR AU - Conder, Marston D. E. AU - Verret, Gabriel TI - Edge-transitive graphs of small order and the answer to a 1967 question by Folkman JO - Algebraic Combinatorics PY - 2019 SP - 1275 EP - 1284 VL - 2 IS - 6 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.82/ DO - 10.5802/alco.82 LA - en ID - ALCO_2019__2_6_1275_0 ER -

%0 Journal Article %A Conder, Marston D. E. %A Verret, Gabriel %T Edge-transitive graphs of small order and the answer to a 1967 question by Folkman %J Algebraic Combinatorics %D 2019 %P 1275-1284 %V 2 %N 6 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.82/ %R 10.5802/alco.82 %G en %F 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. http://www.numdam.org/articles/10.5802/alco.82/

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