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

Background: The aim of this study was to evaluate and compare the apical microleakage around retrograde cavities prepared with ultrasonic technique and filled with (Biodentineâ„¢) Materials and methods: 40 extracted single rooted human permanent maxillary teeth with mature apices were selected. The roots were prepared chemo-mechanically using k-files with crown-down technique and then obturated with lateral condensation gutta-percha technique. Teeth were divided into four main groups according to the cavity preparation method either manual or ultrasonic technique: Group A (n=10): A class I retrograde cavity at root end was prepared with traditional handpeice equipped and placement of Biodentine with manual condensation. Group B (n=10):

Background: The aim of this study was to evaluate and compare the apical microleakage around retrograde cavities prepared with ultrasonic technique and filled with (Biodentineâ„¢) Materials and methods: 40 extracted single rooted human permanent maxillary teeth with mature apices were selected. The roots were prepared chemo-mechanically using k-files with crown-down technique and then obturated with lateral condensation gutta-percha technique. Teeth were divided into four main groups according to the cavity preparation method either manual or ultrasonic technique: Group A (n=10): A class I retrograde cavity at root end was prepared with traditional handpeice equipped and placement of Biodentine with manual condensation. Group B (n=10):

This study compared in vitro the microleakage of a new low shrink silorane-based posterior composite (Filtek™ P90) and two methacrylate-based composites: a packable posterior composite (Filtek™ P60) and a nanofill composite (Filtek™ Supreme XT) through dye penetration test. Thirty sound human upper premolars were used in this study. Standardized class V cavities were prepared at the buccal surface of each tooth. The teeth were then divided into three groups of ten teeth each: (Group 1: restored with Filtek™ P90, Group 2: restored with Filtek™ P60, and Group 3: restored with Filtek™ Supreme XT). Each composite system was used according to the manufacturer's instructions with their corresponding adhesive systems. The teeth were th

Background: The Streptococcus genus are the predominant bacteria in the mouth and the Streptococcus sanguinis is one of them which performing a primary function for expansion of dental biofilm. Gingival and periodontal disorders are caused by dental biofilm, today, there is a necessity to discover naturally presenting antibacterial compounds from herbs with less side effects as a substitutive to the commonly handled chlorohexidine. Thus, the purpose of this study was to assess the antibacterial activity of thymus vulgaris oil on Streptococcus sanguinis bacteria In vitro. Materials and Methods: Human supragingival plaque samples were taken from 10 subjects, then morphological and microscopical examination, bioch

Dental caries (tooth decay) is one of the most prevalent infectious disease and although of multifactorial origin, Streptococcus mutans is considered the principal pathogen in its development (i.e. bacterial processes damage hard tooth structure (enamel, dentine and cementum), producing dental cavities (holes in the teeth). The bactericidal properties of the Nd:YAG laser has been researched analyzing its use in caries prevention and bacterial reduction. One hundred twenty five samples were collected from carious teeth and isolated bacteria were diagnosed using microscopic examination, culture, biochemical tests, and Api 20 strep system. The results of this study showed that a noticeable decrease in the viability of Streptococcus mutans w

The interplay of species in a polluted environment is one of the most critical aspects of the ecosystem. This paper explores the dynamics of the two-species Lokta–Volterra competition model. According to the type I functional response, one species is affected by environmental pollution. Whilst the other degrades the toxin according to the type II functional response. All equilibrium points of the system are located, with their local and global stability being assessed. A numerical simulation examination is carried out to confirm the theoretical results. These results illustrate that competition and pollution can significantly change the coexistence and extinction of each species.

Background: Herbs are being widely explored to discover alternatives to synthetic antibacterial agents.Small Cardamom often referred to as queen of spices because of its very pleasant aroma and taste, have a history as old as human race. Most people use cardamom as a spice and are largely unaware of its numerous health benefits. The purpose of this study was to evaluate the effect of different concentrations of water and alcoholic cardamom extracts on sensitivities, growth, and adherence of Mutans streptococci in vitro. Materials and Methods: In this study, saliva was collected from ten volunteers (College students 18-22 years). Agar well technique was used to study the sensitivities of Mutans streptococci to different concentrations of s

Background: Spices and herbs have been used by many cultures to enhance the flavor and aroma of food and for their medicinal value. Black cardamom is one of these spices widely used in cooking because of its unique taste and powerful flavor. The aim of study was to test the effect of black cardamom on Mutans Streptococci in comparison to chlorhexidine gluconate (0.2%) and de-ionized water. Materials and methods: Dried fruits of black cardamom were extracted by using alcohol (70% ethanol). Saliva was collected from seven volunteers. Agar well technique with different concentrations of black cardamom extracts was used to test the sensitivities of Mutans Streptococci, as well black cardamom extracts effect on viable counts of Mutans Streptococ