The Detour distance is one of the most common distance types used in chemistry and computer networks today. Therefore, in this paper, the detour polynomials and detour indices of vertices identified of n-graphs which are connected to themselves and separated from each other with respect to the vertices for n≥3 will be obtained. Also, polynomials detour and detour indices will be found for another graphs which have important applications in Chemistry.

      The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics.   

Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studie

The main purpose of this paper, is to introduce a topological space , which is induced by reflexive graph and tolerance graph , such that  may be infinite. Furthermore, we offered some properties of  such as connectedness, compactness, Lindelöf and separate properties. We also study the concept of approximation spaces and get the sufficient and necessary condition that topological space is approximation spaces.

 Let  be a connected graph with vertices set  and edges set . The ordinary distance between any two vertices of  is a mapping  from  into a nonnegative integer number such that  is the length of a shortest  path. The maximum distance between two subsets  and  of   is the maximum distance between any two vertices  and  such that  belong to  and  belong to . In this paper, we take a special case of maximum distance when  consists of one vertex and  consists of  vertices, . This distance is defined by: where  is the order of  a graph .

     In this paper, we defined  – polynomials based on

     The result involution graph of a finite group , denoted by  is an undirected simple graph whose vertex set is the whole group  and two distinct vertices are adjacent if their product is an involution element. In this paper, result involution graphs for all Mathieu groups and connectivity in the graph are studied. The diameter, radius and girth of this graph are also studied. Furthermore, several other graph properties are obtained.

Technological development in the last years leads to increase the access speed in the internet networks that allow a huge number of users watching videos online.

     Video streaming important type in the real-time video sessions and one of the most popular applications in networking systems.  The Quality of Service (QoS) techniques give us indicate to the effect of multimedia traffic on the network performance, but this techniques do not reflect the user perception. Using QoS and Quality of Experience (QoE) together can give guarantee to the distribution of video content according to video content characteristics and the user experience .

     To measure the users’ perceptio

The function of internal auditing has become an important function that aims at achieving objectives that are compatible with these developments and changes that have occurred in many countries in the world, which required the emergence of professional associations and institutes in the profession of internal auditing. Improve the guideline of the internal audit units issued by the Federal Audit Bureau to enhance the efficiency of internal audit performance in Iraqi government units. The researchers adopted the statistical method of proving the hypothesis by constructing a questionnaire that included three main axes: supporting the senior management in adopting the current guide, and the second being the importance of improving t

   This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.  

 In this paper, we introduce and discuss an algorithm for the numerical solution of some kinds of fractional integral and fractional integrodifferential equations. The algorithm for the numerical solution of these equations is based on iterative approach. The stability and convergence of the fractional order numerical method are described. Finally, some numerical examples are provided to show that the numerical method for solving the fractional integral and fractional integrodifferential equations is an effective solution method.

The images and drawings reduce the intellectual, symbolic and cognitive dimensions inside them that make them an intermediary that imposes itself on the educational method, as they have become responsive to all the needs of the student in the modern era unlike the previous periods. The artistic direction of the illustrations in the scientific books meets the educational and pedagogical needs of the learner and their frame in an illustrative educational method that contributes in developing the student's abilities to benefit from the scientific curricula in the age of scientific and cognitive development.

Here, the researcher finds that the artistic direction of the illustrations lacks the achievement of scientific and technical p