In the title compound, C13H7Cl3O2, the dihedral angle between the benzene rings is 82.1 (2)°. The dihedral angle between the CO2 group and its carbon-bonded ring is 14.50 (19)° In the crystal, aromatic π-π stacking inter-actions [minimum ring centroid separation = 3.604 (2) Å] occur.

In the title compound, C12H11NO4, the dihedral angle between the benzene and isoxazole rings is 42.52 (8)°. The carb-oxy-lic acid group is close to being coplanar with the isoxazole ring [dihedral angle = 5.3 (2)°]. In the crystal, inversion dimers linked by pairs of O-H⋯O hydrogen bonds generate R2(2)(8) loops.

Assuming that G is a finite group and H subgroup of G, the graph known as relative coprime with respect to (denoted Γ_(G,H)) has vertices corresponding elements G. Two distinct x y are adjacent by an edge if only (|x|,|y|)=1 or belongs H. This paper will focus on finding general formula for some topological indices dihedral group. The study in theory offers valuable insights into structural pro...

Let R be a finite ring. In this paper, we mainly explore the conditions to ensure graph BΓn defined by system of equations {fi|i=2,⋯,n} Cayley or Hamiltonian graph. More precisely, prove that is with G=⟨ϕ,A⟩ group dihedral type if and only Fn={fi|i=2,⋯,n} graphic in . As an application, well-known Lovász Conjecture, which states any connected has Hamilton cycle, holds for Fn field GF(pk).

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...

We consider the degree-diameter problem for Cayley graphs of dihedral groups. We find upper and lower bounds on the maximum number of vertices of such a graph with diameter 2 and degree d. We completely determine the asymptotic behaviour of this class of graphs by showing that both limits are asymptotically d/2.

The category of rational O(2)-equivariant spectra splits as a product of cyclic and dihedral parts. Using the classification of rational G-equivariant spectra for finite groups G , we classify the dihedral part of rational O(2)-equivariant spectra in terms of an algebraic model.

Let n be a natural number larger than two. Let D2n = ⟨r, s ∶ r = s = e, srs = r⟩ be the Dihedral group, and κ an n-dimensional unitary representation of D2n acting in C as follows. (κ(r)v)(j) = v((j−1) mod n) and (κ(s)v)(j) = v((n − j) mod n) for v = (v0,⋯, vn−1) ∈ C. For any representation which is unitarily equivalent to κ, we prove that when n is prime there exists a Zariski open subset E of...