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

The purpose of this study is to develop and assess the effectiveness of exercises using heavy and hanging ropes for handball players, focusing on enhancing specific physical abilities and shooting accuracy. The research addresses the gap in training methodologies by comparing the effects of heavy rope exercises versus hanging rope exercises. An experimental design was used in two equal groups, besides pre-testing and post-testing. The study involved 16 players from the School of Handball for the season 2022–2023. The sample included 14 players, who were then randomly divided into two experimental groups of 7 each. The first group performed heavy rope exercises, while hanging rope exercises were included in the plan of the second group. Th

Background: The PMMA polymer denture base materials are low mechanical properties, adaptation of the denture base to underlying tissue is important for retention and stability of denture. The aim of the study was toevaluate the effect of mixtureZrO2-Al2O3 nanoparticles on impact strength, transverse strength, hardness, roughness, denture base adaptation of heat cured acrylic resin denture base material. Materials and methods: One hundred (100) specimens were prepared, the specimens were divided into five groups (20 specimens to each) according to the test type, each group was subdivided in to two subgroups (control and experimental) each subgroup consist of 10 specimens, the experimental group included mixture of 2% (ZrO2-Al2O3ratio2:1) b

Background: Polymethyl methacrylate (PMMA) is the most commonly used material in denture fabrication. The material is far from ideal in fulfilling the mechanical requirements. Midline fracture; poor thermal conductivity and water sorption, are common problem in this material. The purpose of this study was to evaluate the effect of addition of surface treated Aluminum oxide nano fillers on some properties of heat cured (PMMA). Materials and methods: In addition to controlled group of heat cured PMMA the silanized (Al2O3) nanoparticles was added to PMMA powder by weight in three different percentages 1wt%, 2wt% and 3wt%, mixed by probe ultra-sonication machine. 200 specimens were constructed and divided into 5 groups according to the test (e

The study involved preparing a new compound by combining between 2- hydroxybenzaldehyde and (Z)-3-hydrazineylideneindolin-2-one resulting in Schiff bases and metal ions: Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) forming stable minerals-based-Schiff complexes. The formation of resulting Schiff bases is detected spectrally using LC-Mss which gave corresponding results with theoretical results, 1H-NMR proves the founding of N=CH signal, FT-IR indicates the occurrence of imine band and UV-VIs mean is proved the ligand formation. On the other hand, minerals-based-Schiff was characterized using the same spectral means that relied with ligand (Schiff bases). Those means gave satisfactory results and proved the suggested distinguishable geometries

The research discusses one of the most critical issues of corporate finance which is related to asset utilization efficiency. Researchers used internal growth rate as independent variable (Proxy of asset utilization efficiency) and sustainable growth rate-dependent variable (proxy of stockholders wealth). According to these two variables, researchers formulate major hypotheses (There is no significant effect of internal growth rate on sustainable growth rate), as well as two sub-hypotheses, examine the components of major variables. Sample of Iraqi industrial companies which listed in the Iraqi stock exchange selected to test and examine main hypotheses. Result of simple and multiple regressions explain there is a significant effect of i

BACKGROUND: Hospital training courses for pharmacy students were required to prepare students to meet the challenges of real-world hospital work. AIM: Because there have been few studies on the efficacy of such courses, we aimed to recognize recent graduates’ perceptions, benefits, and factors influencing the quality of hospital training courses for pharmacy students. METHODS: A qualitative study using a phenomenology approach was conducted in 2022 and included several hospitals in Baghdad, Iraq, using in-depth face-to-face individual-based semi-structured interviews. Until saturation, a convenient sample of recently graduated pharmacists was included. The obtained data were analyzed using a thematic content analysis approach

This paper presents a comparison study on thermal performance conic cut twist tape inserts in laminar flow of nanofluids through a constant heat fluxed tube. Three tape configurations, namely, quadrant cut twisted tape (QCT), parabolic half cut twisted tape (PCT), and triangular cut twisted (VCT) of twist ratioy= 2.93 and cut depthde= 0.5 cm were used with 1% and 2% volume concentration of SiO₂/water and TiO

The H-Point Standard Addition Method (H-PSAM) has been applied for spectrophotometric simultaneous determination of Cimetidine and Erythromycin ethylsuccinate using Bromothymol Blue (BTB) as a chromogenic complexing agent in a buffer solution at pH 5.5.

Background: Change in palatal vault shape and Reinforcement of high impact acrylic denture base resin may in turn affect the dimensional accuracy of acrylic resin and affecting the fitness of the denture. The aim of study is to evaluate the effect of fiber reinforcement for high-impact acrylic resin denture base with different palatal vault shapes on linear dimensional change and effect of palatal vault shapes on linear dimensional changes of non-reinforced and fiber reinforced high impact denture base acrylic resin Material and method: Three different palatal vault shapes were prepared on standard casts using CNC (computer numerical control) machine. 60 samples of heat polymerized high impact acrylic resin maxillary denture base were fabri