Finite edge-primitive graphs of prime valency

On Edge-Primitive Graphs With Soluble Edge-Stabilizers

“…In this case, noting that |T {u,v} :T uv | ≤ 2, we have |T v | = 2 4 p f ((q 2 +1) 2 /(2, q − 1) 2 ) or 2 3 p f ((q 2 +1) 2 /(2, q − 1) 2 ). Let M be a maximal subgroup of T with T v ≤ M. By [13], since |M| is divisible by [24] following quadruples:…”

On edge-primitive and 2-arc-transitive graphs

“…As consequence of Theorems 3.3 and 3.7, an edge-primitive graph of prime valency is 2-arc-transitive, and then it has almost simple automorphism group if it is not a complete bipartite graph. See also [21]. [17,Lemma 2.3], and so G uv = 1, which contradicts Corollary 3.2.…”

“…Besides, the almost groups PSU (3,5).2, M 22 .2, J 2 .2 and McL.2 all have representations on edge-primitive graphs. The reader may refer to [11,12,18,21,26] for more examples of edge-primitive graphs which have almost simple automorphism groups. Of course, using the constructions given in [9], one can easily construct examples of edge-primitive graphs with automorphism groups not almost simple.…”

On edge-primitive graphs with soluble edge-stabilizers

“…Besides, the almost groups PSU (3,5).2, M 22 .2, J 2 .2 and McL.2 all have representations on edge-primitive graphs. For more examples, the reader may refer to [9,10,16,21,26].…”