On tetravalent normal edge-transitive Cayley graphs on the modular group

Abstract

) is transitive on edges of Γ , where ρ(G) is a subgroup of Aut(Γ) isomorphic to G . We determine all connected tetravalent normal edge-transitive Cayley graphs on the modular group of order 8n in the case that every element of S is of order 4n .

Tetravalent non-normal Cayley graphs of order 5p^2

“…In [8], all the normal edge-transitive Cayley graphs of modular groups of order 8n, where n is a natural number, are determind and in [1,5,6] all the tetravalent edge-transitive Cayley graphs on non-Abelian groups of order p 2 , 3p 2 , 4p 2 are determined. In [11] all connected cubic non-normal Cayley graphs of order 2p 2 are studied.…”

ON CONNECTED TETRAVALENT NORMAL EDGE-TRANSITIVE CAYLEY GRAPHS OF NON-ABELIAN GROUPS OF ORDER 5p^2

“…Normal edge-transitive Cayley graphs on non-Abelian groups of order p 2 , 3p 2 , 4p 2 and modular groups of order 8n , where p is prime and n is a natural number, were studied in [2,5,6,8]. In this paper, motivated by [2,6], we determine the structure of Cayley graphs on non-Abelian groups of orders 5p 2 with cyclic Sylow p -subgroup with respect to tetravalent sets with same-order elements, where p is a prime number.…”