For a finite group G, let Z(G) be the centre of G. Then non-commuting graph on denoted by ΓG, has G\Z(G) as its vertex set with two distinct vertices vp and vq joined an edge whenever vpvq ≠ vqvp. The degree sum matrix is square whose (p,q)-th entry dvp + dvq p different from q, otherwise, it zero, where dvi vi. This study presents general formula for energy, EDS (ΓG), dihedral groups order 2n,...

The study of perfect state transfer on graphs has attracted a great deal attention during the past ten years because its applications to quantum information processing and computation. Perfect is understood be rare phenomenon. This paper establishes necessary sufficient conditions for bi-Cayley graph having over any given finite abelian group. As corollaries, many known new results are obtained...

There are well known necessary conditions for the existence of a generalized Bhaskar Rao design over a group G, with block size k = 3. We prove that they are sufficient for nilpotent groups G of even order, and in particular for 2-groups. In addition, we prove that they are sufficient for semi-dihedral groups.

Let D2N be the dihedral group of order 2N , Dic4M the dicyclic group of order 4M , SD2m the semidihedral group of order 2 m, and M2m the group of order 2 m with presentation M2m = 〈α, β | α 2m−1 = β2 = 1, βαβ−1 = α2 m−2+1〉. We classify the orbits in Dn 2N , Dic n 4M , SD n 2m , and M n 2m under the Hurwitz action.

in this paper we define s algebras and show that every finite group can be found in some s algebra.  we define and study the s degree of a finite group and determine the s degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $d_p$.

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.