The arc-types of Cayley graphs

On 2-arc-transitivity of Cayley graphs

Arc { Transitive Non { Cayley Graphs from Regular

We prove that the underlying graphs of p-gonal r-valent orientably regular maps are arc-transitive but non-Cayley if r 3 and p is a prime greater than r(r ? 1).

On the distance eigenvalues of Cayley graphs

In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...

On 2-arc-transitive Cayley Graphs of Dihedral Groups

Slovenija Abstract A partial extension of the results in 1], where 2-arc-transitive cir-culants are classiied, is given. It is proved that a 2-arc-transitive Cayley graph of a dihedral group is either a complete graph or a bi-partite graph.

Arc–transitive Non–cayley Graphs from Regular Maps

We prove that the underlying graphs of p-gonal r-valent orientably regular maps are arc-transitive but non-Cayley if r ≥ 3 and p is a prime greater than r(r − 1).