Generalized Cayley Digraphs

On Hamilton Circuits in Cayley Digraphs over Generalized Dihedral Groups

In this paper we prove that given a generalized dihedral group DH and a generating subset S, if S∩H 6= ∅ then the Cayley digraph → Cay(DH , S) is Hamiltonian. The proof we provide is via a recursive algorithm that produces a Hamilton circuit in the digraph.

Cayley Digraphs from Complete Generalized Cycles

The complete generalized cycle G(d, n) is the digraph which has Zn × Zd as the vertex set and every vertex (i, x) is adjacent to the d vertices (i + 1, y) with y ∈ Zd . As a main result, we give a necessary and sufficient condition for the iterated line digraph G(d, n, k) = Lk−1G(d, n), with d a prime number, to be a Cayley digraph in terms of the existence of a group0d of order d and a subgrou...

A Class of Generalized Cayley Digraphs Induced by Quasigroups

We generalize the results in [13] to produce new classes of generalized cayley graphs induced by quasigroups. Mathematics Subject Classification: 05C25

Some non-normal Cayley digraphs of the generalized quaternion group of ertain orders

Some Non-Normal Cayley Digraphs of the Generalized Quaternion Group of Certain Orders

We show that an action of SL(2, p), p ≥ 7 an odd prime such that 4 6 | (p − 1), has exactly two orbital digraphs Γ1, Γ2, such that Aut(Γi) admits a complete block system B of p + 1 blocks of size 2, i = 1, 2, with the following properties: the action of Aut(Γi) on the blocks of B is nonsolvable, doubly-transitive, but not a symmetric group, and the subgroup of Aut(Γi) that fixes each block of B...