Edge-primitive Graphs Of Four Times A Prime Power

Characterizing edge-primitive graphs with specific order is an effective way to study edge-primitive graphs.In the work of Pan and Wu et al.[34,35],edge-primitive graphs with orders of prime power and twice a prime power were com-pletely classified.Based on the work of Pan and Wu et al.,we classified edge-primitive graphs with order four times a prime power in this thesis.The research strategy of this thesis is to consider the genetic properties of graphs,and the study of edge-primitive graphs is reduced to the cases of vertex-primitive and vertex-biprimitive graphs.The main result of this thesis is that in addition to the infinite classes of complete graphs and complete bipartite graphs,the edge-primitive graphs of order four times a prime power have only three scattered graphs which have almost simple groups with almost simple groups as their automorphism groups with socle J₂and HS respectively.