Automorphisms of groups and isomorphisms of Cayley digraphs

Isomorphisms and automorphism groups of a class of Cayley digraphs on Abelian groups

In this paper, we investigate problems about isomorphisms and automorphism groups of Cayley digraphs. A class of Cayley digraphs, corresponding to the so-called CDI-subsets, for which the isomorphisms are uniquely determined by the group automorphisms is characterized. Their automorphism groups are also characterized.

Automorphism groups and isomorphisms of Cayley digraphs

Large Cayley digraphs and bipartite Cayley digraphs of odd diameters

Let Cd,k be the largest number of vertices in a Cayley digraph of degree d and diameter k, and let BCd,k be the largest order of a bipartite Cayley digraph for given d and k. For every degree d ≥ 2 and for every odd k we construct Cayley digraphs of order 2k ( ⌊d2⌋ )k and diameter at most k, where k ≥ 3, and bipartite Cayley digraphs of order 2(k − 1) ( ⌊d2⌋ )k−1 and diameter at most k, where k...

Isomorphisms and normality of Cayley digraphs of A5

It is proved that each 2-element generating set of A5 is a CI-subset and that the corresponding Cayley digraph is normal. It is furthermore proved that for each 3-element generating set of A5 the corresponding Cayley digraph is normal.

On isomorphisms of Cayley digraphs on dicyclic groups

In this paper we prove that for any m E {I, 2, 3}, the dicyclic group B 4n (n i=2) is an m-DCI group if and only if n is odd.