Edge-transitive graphs of small order and the answer to a 1967 question by Folkman

Conder, Marston D. E.; Verret, Gabriel

Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1275-1284.

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 $1$.

Classification : 05E18, 05C25, 20B25
Mots clés : arc-transitive graph, edge-transitive graph, semi-symmetric graph, twin-free graph

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