In this paper,we classify connected arc-transitive graphs of valency 1l and of order 4n,where n is an odd square-free integer.In particular,there are four infinite families of such graphs,which have a minimal arc-tran...In this paper,we classify connected arc-transitive graphs of valency 1l and of order 4n,where n is an odd square-free integer.In particular,there are four infinite families of such graphs,which have a minimal arc-transitive automorphism group isomor-phic to PSL(2,r),PGL(2,r),Z2×PSL(2,r)and PSL(2,r)×Z11 separately,where r=±1(mod 11)is a prime.Moreover,examples for each class are constructed.展开更多
基金National Natural Science Foundation of China(12061089,11861076,11701503,12161021,11761079)Natural Science Foundation of Yunnan Province(2019FB139,202201AT070022).
文摘In this paper,we classify connected arc-transitive graphs of valency 1l and of order 4n,where n is an odd square-free integer.In particular,there are four infinite families of such graphs,which have a minimal arc-transitive automorphism group isomor-phic to PSL(2,r),PGL(2,r),Z2×PSL(2,r)and PSL(2,r)×Z11 separately,where r=±1(mod 11)is a prime.Moreover,examples for each class are constructed.
