A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.  For a simple undirected graph G with order n, and let  denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where C

An experiment was conducted in the Date Palm Research Units labs / College of Agricultural Engineering Sciences / University of Baghdad to assess the tolerance toward salinity stress in potato after two mutagens treatments in vitro. Potato cv. Arizona and Rivera nodal segments were irradiated with four dosages of gamma rays at 0, 10, 20, and 30 Gray and immersed in (EMS) with four concentrations included 0, 10, 20, and 30 mM. The survival rates after mutagenesis treatments were calculated and 449 lines were obtained. The lines were tested for salinity tolerance by growing in MS medium supplemented with four concentrations of NaCl at 0, 100, 150, and 200 mM and data were analyzed according to the CRD with 10 replicates and means were

The stability and releasing profile of 2:1 core: wall ratio ibuprofen microcapsules prepared by aqueous coacervation (gelatin and acacia polymers coat) and an organic coacervation methods (ethyl cellulose and sodium alginate polymers coat) in weight equivalent to 300mg drug, were studied using different storage temperatures 40°C, 50°C ,60°C and refrigerator temperature 4°C in an opened and closed container for three months (releasing profile) and four months (stability study).It was found that, these ibuprofen microcapsules were stable with expiration dates of 4.1 and 3.1 years for aqueous and an organic method respectively.Aqueous prepared ibuprofen microcapsules were found more stable than those microcapsules prepared by or

Polycaprolactone is one of the natural biodegradable polymers mainly used in bioplastics production for packaging, usually composed of non-toxic compounds and biodegradable. The aim was to examine the role of zinc oxide (ZnO) nanopowder on the,wettability , thermal and anti-bacterial effect nanocomposites.  Pure PCL and PCL-based bio- nanocomposites doped with various ratios of ZnO nanoparticles from 0% to 5wt% were prepared through the arrangement of throwing procedure.  The results show that wettability properties in relation to ideal PCL and that they were increasingly hydrophobic from 57º.8 to 69º.53 because add ZnO  nanocomposites,the thermal stability between 300 and 400 ° C makes them perfect for the application

This paper is illustrates the sufficient conditions of the uniformly asymptotically stable and the bounded of the zero solution of fifth order nonlinear differential equation with a variable delay τ(t)

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system.

It is well known that the spread of cancer or tumor growth increases in polluted environments. In this paper, the dynamic behavior of the cancer model in the polluted environment is studied taking into consideration the delay in clearance of the environment from their contamination. The set of differential equations that simulates this epidemic model is formulated. The existence, uniqueness, and the bound of the solution are discussed. The local and global stability conditions of disease-free and endemic equilibrium points are investigated. The occurrence of the Hopf bifurcation around the endemic equilibrium point is proved. The stability and direction of the periodic dynamics are studied. Finally, the paper is ended with a numerical simul