This paper aims to develop a theory for studying Cayley graphs, especially for those with a high degree of symmetry. The theory consists of analysing several types of basic Cayley graphs (normal, bi-normal, and corefree), and analysing several operations of Cayley graphs (core quotient, normal quotient, and imprimitive quotient). It provides methods for constructing and characterising various c...

In this paper, the notion of fuzzy n-polygroups (Fn -polygroups) is introduced and some related properties are investigated. In this regards, the concepts of normal  F-subpolygroups and homomorphisms of Fn-polygroups are adopted. Also, the quotient of Fn-polygroups by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Fn-polygroups p...

Objectives: The aim of this study was to compare the fine motor development between Low Birth Weight (LBW) infants and Normal Birth Weight infants (NBW) at the age of 8-12 months by using the Peabody Developmental Motor Scale-2 (PDMS-2) . Methods: This was a non experimental and cross sectional study which was conducted on the 18 LBW infants and 14 normal infants. By referring to the profile...

the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...

A brief comment about items (3) and (4). If H is a subgroup of G the inclusion map is an injective homomorphism from H to G . On the other hand, the image of an injective homomorphism α : H −→ G is a subgroup that is isomorphic to H . So the study of injective homomorphisms is (up to isomorphism) the study of subgroups. After studying subgroups, we defined normal subgroup and showed several equ...

We generalize the well-known numerical criterion for projective spaces by Cho, Miyaoka and Shepherd-Barron to varieties with at worst quotient singularities. Let X be a normal projective variety of dimension n ≥ 3 with at most quotient singularities. Our result asserts that if C · (−KX) ≥ n + 1 for every curve C ⊂ X, then X ∼= P .

A 1nite graph is said to be locally-quasiprimitive relative to a subgroup G of automorphisms if, for all vertices , the stabiliser in G of is quasiprimitive on the set of vertices adjacent to . (A permutation group is said to be quasiprimitive if all of its non-trivial normal subgroups are transitive.) The graph theoretic condition of local quasiprimitivity is strictly weaker than the condition...

The symmetry properties of mathematical structures are often important for understanding these structures. Graphs sometimes have a large group of symmetries, especially when they have an algebraic construction such as the Cayley graphs. These graphs are constructed from abstract groups and are vertex-transitive and this is the reason for their symmetric appearance. Some Cayley graphs have even ...