. Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper,we introduce the generalized Cayley graph denoted by  which is a graph with a vertex set consisting of all column matrices  in which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of the similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and  and m . We aim to provide some basic properties of the new graph and determine the structure of  when  is a complete graph  for every , and n, m  .

        The purpose of this work is to construct complete (k,n)-arcs in the projective 2-space PG(2,q) over Galois field GF(11) by adding some points of index zero to complete (k,n–1)arcs 3 ï‚£ n ï‚£ 11.         A (k,n)-arcs is a set of k points no n + 1 of which are collinear.         A (k,n)-arcs is complete if it is not contained in a (k + 1,n)-arc

A (k,n)-arc A in a finite projective plane PG(2,q) over Galois field GF(q), q=pⁿ for same prime number p and some integer n≥2, is a set of k points, no n+1 of which are collinear.  A (k,n)-arc is complete if it is not contained in a(k+1,n)-arc.  In this paper, the maximum complete (k,n)-arcs, n=2,3 in PG(2,4) can be constructed from the equation of the conic.

We define a new concept, called " generalized right  -derivation", in near-ring and obtain new essential results in this field. Moreover we improve this paper with examples that show that the assumptions used are necessary.

         Let  be any group with identity element (e) . A subgroup intersection graph of  a subset  is the Graph with V ( ) =  - e and two separate peaks c and d contiguous for c and d if and only if      , Where  is a Periodic subset of resulting from  . We find some topological indicators in this paper and Multi-border (Hosoya and Schultz) of   , where    ,  is aprime number.

In the present investigation, new polymers of Poly [ N - acryl - N - sulfonic acid - N\ yL - 2 - substitute - 4 - oxo - thiazolidine ] Maleic and Succinic diimide were synthesized by seven steps; first step includes esterification of different cyclic anhydride, using one mole of absolute methanol in the presence few drops of conc. H2SO4, yielded mono group ester [I] , which was reaction with thionyl chloride to give ester acid chloride [II] .Then reacted with sulfanilic acid to product compound [III] , which was condensation with hydrazine hydrate to give acid hydrazide [IV] . The new different Schiff bases [V-VIII] were synthesized by reaction of acid hydraizide with different (aliphatic and aromatic) aldehyedes and ketones in the prese

A new Schiff base, 2-N( 4- N,N – dimethyl benzyliden )5 – (p- methoxy phenyl) – 1,3,4- thiodiazol ,and their metal complexes Cu (Π) ,Ni (Π),         Fe (III) , Pd (Π) , Pt (IV) , Zn(Π) ,V(IV) and Co (Π) , were synthesized. The prepared complexes were identified and their structural geometries were suggested by using flam atomic absorption technique , FT-IR and Uv-Vis spectroscopy, in addition to magnetic susceptibility and conductivity measurements. The study of the nature of the complexes formed in ethanol solution , following the mole ratio method , gave results which were compared successfully with those obtained from the isolated solid state studied. Structur

In this paper, we will give another class of normal operator which is (K-N)*
quasi-n-normal operator in Hilbert space, and give some properties of this concept
as well as discussion the relation between this class with another class of normal
operators.

 The preparation of some new coordination compounds for nikel (II), manganese (II), copper (II), cobalt (II)and mercury (II), with ligand obtained from Benzoinand2-amino pyridine.The ligand[6-(2-hydroxy-1,2-diphenylethylideneamino)pyridin-3-ylium)](L) was made from reactin ethanol with metal salts in (1:1)(metal : ligand)ratio.[MLCl] was the inclusive formula of the complexes where M= Mn(II),Co(II),Ni(II),Cu(II) and Hg(II). Metal analysis by electronic spectra, atomic absorption ,infrared spectra, 1H&13C-NMR(only ligand)spectral studies, magnetic moment and molar conductance measurements used to describe the compounds.The determinations indicated that the ligand coordinates with the metal (II) ion in neutral tridentate manner th