In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

Let A ⊆ V(H) of any graph H, every node w of H be labeled using a set of numbers; , where d(w,v) denotes the distance between node w and the node v in H, known as its open A-distance pattern. A graph H is known as the open distance-pattern uniform (odpu)-graph, if there is a nonempty subset A ⊆V(H) together with  is the same for all . Here  is known as the open distance pattern uniform (odpu-) labeling of the graph H and A is known as an odpu-set of H. The minimum cardinality of vertices in any odpu-set of H, if it exists, will be known as the odpu-number of the graph H. This article gives a characterization of maximal outerplanar-odpu graphs. Also, it establishes that the possible odpu-number of an odpu-maximal outerplanar graph i

Contemporary developments in various sciences and the impact of technological changes require an integrated vision of the activities and work of the organization in Iraq in light of the high costs of products and their low quality compared to imported products of high quality and low cost, and the need to use modern cost techniques based on a clear and specific philosophy that contributes to increasing the efficiency and effectiveness of management In the business environment and how it can contribute to reducing product costs and being environmentally friendly at the same time, it is no secret that the main goal of most organizations is to maximize profitability and reduce costs to the minimum, but this matter is not achieved autom

The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.

This study had succeeded in producing a new graphical representation of James abacus called nested chain abacus. Nested chain abacus provides a unique mathematical expression to encode each tile (image) using a partition theory where each form or shape of tile will be associated with exactly one partition.Furthermore, an algorithm of nested chain abacus movement will be constructed, which can be applied in tiling theory.

The addition of new reactive sites on the surface area of the inert sand, which are represented by layered double hydroxide nanoparticles, is the primary goal of this work, which aims to transform the sand into a reactive material. Cetyltrimethylammonium bromide (CTAB) surfactant is used in the reaction of calcium extracted from solid waste-chicken eggshells with aluminum prepared from the cheapest coagulant-alum. By separating amoxicillin from wastewater, the performance of coated sand named as "sand coated with (Ca/Al-CTAB)-LDH" was evaluated. Measurements demonstrated that pH of 12 from 8, 9, 10, 11, and 12, CTAB dosage of 0.05 g from 0, 0.03, 0.05, and 0.1 g, ratio of Ca/Al of 2 from 1, 2, 3, and 4, and mass of sand of 1 g/50 mL from