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 , and all bipartite edge-transitive graphs of order up to . 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 and valency , the ratio can be arbitrarily close to .
Accepted:
Revised after acceptance:
Published online:
DOI: 10.5802/alco.82
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}, 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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