A graph is vertex− transitive or symmetric if its automorphism group acts transitively on
vertices or ordered adjacent pairs of vertices of the graph, respectively. Let G be a finite …

A graph is vertex-transitive if its automorphism group acts transitively on its vertices. A vertex-
transitive graph is a Cayley graph if its automorphism group contains a subgroup acting …

It is shown that a minimal normal subgroup of a transitive permutation group of square-free
degree in its induced action is simple and quasiprimitive, with three exceptions related to A5 …

A cubic graph Γ is G-arc-transitive if G≤ Aut (Γ) acts transitively on the set of arcs of Γ, and G-
basic if Γ is G-arc-transitive and G has no non-trivial normal subgroup with more than two …

A complete classification is given of finite primitive permutation groups which contain a
regular subgroup of square-free order. Then a collection\cal P\cal N\cal C of square-free …

Given a finite simple graph Γ on n vertices its complementary prism is the graph Γ Γ¯ that is
obtained from Γ and its complement Γ¯ by adding a perfect matching where each its edge …

On Non-Cayley Vertex-Transitive Graphs of Order a Product of Three Primes Page 1 Journal of
Combinatorial Theory, Series B 81, 1 19 (2001) On Non-Cayley Vertex-Transitive Graphs of …

Cayley graphs are constructed using groups. This chapter discusses algebraic and graph-
theoretic aspects of finite Cayley graphs. The algebraic aspects include recognition …

Marušič (Ann. Discrete Math. 27 (1985) 115) proved that all vertex-transitive graphs of order
pk are Cayley graphs for each prime p and k= 1, 2, or 3, and constructed a non-Cayley …

A positive integer n is a Cayley number if every vertex-transitive graph of order n is a Cayley
graph. In 1983, Dragan Marušič posed the problem of determining the Cayley numbers. In …