Perfect quantum state transfer plays a crucial role in information processing and computation. There has been extensive study of perfect on Cayley graphs over abelian groups. In this paper, we consider the existence semi-dihedral groups which are non-abelian Using representations groups, provide some necessary sufficient conditions for admitting transfer. By those conditions, present examples a...

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...

This research is about the group coverings of subsets finite non-abelian groups and its application in field cryptography. Group abelian has been researched over years it many applications various fields. The popularity internet increased rapidly cryptography become more important as ensures privacy security users network. A cryptosystem a structure consisting several cryptographic primitives. ...

Let n, x be positive integers satisfying 1 < x < n. Let Hn,x be a group admitting a presentation of the form 〈a, b | a = b = (ba) = 1〉. When x = 2 the group Hn,x is the familiar dihedral group, D2n. Groups of the form Hn,x will be referred to as generalized dihedral groups. It is possible to associate a cubic Cayley graph to each such group, and we consider the problem of finding the isoperimet...

Almost all known results on difference sets need severe restrictions on the parameters. The main purpose of this paper is to provide an asymptotic nonexistence result free from any assumptions on the parameters. The only assumption we make is that the underlying group is dihedral. Difference sets originally mainly were studied in cyclic groups where they exist in abundance. For example, for any...

The dihedral group is defined by 〈x, y | x = y = e, xy = yx−1〉 for n ≥ 3 and has order 2n. In this note four families of 2-critical sets are presented for the Latin square based on this group for even n.

In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group Dn, extending earlier work by the author and Criel Merino. In particular, we show that the critical group of such a graph can be decomposed in terms of the critical groups of the quotients of the graph by certain subgroups of the automorphism group. This is analogous to a t...

We present a description, including a characterization, of the complete cd-index of dihedral intervals. Furthermore, we describe a method to compute the complete cd-index of intervals in universal Coxeter groups. To obtain such descriptions, we consider Bruhat intervals for which Björner and Wachs’s CL-labeling can be extended to paths of different lengths in the Bruhat graph. While such an ext...