Large Cayley digraphs and bipartite Cayley digraphs of odd diameters

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...

Large butterfly Cayley graphs and digraphs

We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large k and for values of d taken from a large interval, the largest known Cayley graphs and digraphs of diameter k and degree d. Another method yields, for sufficiently large k and infinitely many values of d, Cayley graphs and digraphs of diame...

Generalized Cayley Digraphs

In this paper we introduce a new class of digraphs induced by groups. These digraphs can be considered as the generalization of Cayley digraphs. Moreover, various graph properties are expressed in terms of algebraic properties. This did not attract much attention in the literature. Mathematics Subject Classification: 05C25

Cayley digraphs and lexicographic product ∗

In this paper, we prove that a Cayley digraph Γ = Cay(G, S) is a nontrivial lexicographical product if and only if there is a nontrivial subgroup H of G such that S \ H is a union of some double cosets of H in G.

Automorphism groups and isomorphisms of Cayley digraphs