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A graph X is symmetric if its automorphism group is transitive on the arc set of the graph. Let p and q be two prime integers. In this paper, a complete classification is determined of connected pentavalent symmetric graphs of order 8pq. [ABSTRACT FROM AUTHOR]

A graph X is symmetric if its automorphism group is transitive on the arc set of the graph. Let p and q be two prime integers. In this paper, a complete classification is determined of connected pentavalent symmetric graphs of order 8pq. [ABSTRACT FROM AUTHOR]

A Cayley graph Γ = Cay(G; S) is called normal edge-transitive (are-transitive) for G if NAut(Γ)(G) (the full automorphism group Aut(Γ) of Γ) acts transitively on edges (arcs). In this paper we determine normal edge-transitive and arc-transitive connected undirected Cayley graphs on non-cyclic abelian groups of certain valency. [ABSTRACT FROM AUTHOR]

For a group G, and a subset S of G such that 1G ∉ S, let Γ = Cay(G, S) be a Cayley graph. Then Γ is said to be arc-transitive, if Aut(Γ) is transitive on arc set. In this paper we give a complete classification for arc-transitive Cayley graphs of valency five on finite abelian groups. [ABSTRACT FROM AUTHOR]

For a group G, and a subset S of G such that 1G ∉ S, let Γ = Cay(G, S) be a Cayley graph. Then Γ is said to be normal edge transitive, if NAut(Γ) (G) is transitive on edges. In this paper we determine all edge transitive Cayley graphs of finite abelian group with valency at most five, which are not normal edge transitive. This is a partial answer to a question of Praeger. [ABSTRACT FROM AUTHOR]