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

Among the metaheuristic algorithms, population-based algorithms are an explorative search algorithm superior to the local search algorithm in terms of exploring the search space to find globally optimal solutions. However, the primary downside of such algorithms is their low exploitative capability, which prevents the expansion of the search space neighborhood for more optimal solutions. The firefly algorithm (FA) is a population-based algorithm that has been widely used in clustering problems. However, FA is limited in terms of its premature convergence when no neighborhood search strategies are employed to improve the quality of clustering solutions in the neighborhood region and exploring the global regions in the search space. On the

This research aims to show the sight at the importance of the private banking sector in Iraq and its role in financing of the investment projects , of the ability of Central Bank's decision to increase the minimum limit of capital for private banks to provide support to the economic activity and the development in Iraq. In addition to illustrate the importance of the capital increase, with a, and taking into notice the most important determinants that can stand in front of these banks in the beginning of the decision implementation, which in turn can lead to the most important proceedings that can contribute in the support of banks to implementation the decision.  Also, the research has highlighted the most important ways through wh

In this paper, Nordhaus-Gaddum type relations on open support independence number of some derived graphs of path related graphs under addition and multiplication are studied.

This paper proposes a new method Object Detection in Skin Cancer Image, the minimum
spanning tree Detection descriptor (MST). This ObjectDetection descriptor builds on the
structure of the minimum spanning tree constructed on the targettraining set of Skin Cancer
Images only. The Skin Cancer Image Detection of test objects relies on their distances to the
closest edge of thattree. Our experimentsshow that the Minimum Spanning Tree (MST) performs
especially well in case of Fogginessimage problems and in highNoisespaces for Skin Cancer
Image.
The proposed method of Object Detection Skin Cancer Image wasimplemented and tested on
different Skin Cancer Images. We obtained very good results . The experiment showed that

The aim of this research is to investigate the skills of the chemistry students from the Ibn Al-Haytham Education college of pure sciences in Baghdad in understanding and constructing graphical representations of data. The research sample consisted of (101) male and female students in their fourth year of study during the 2016-2017 academic year. This sample represents 71% of the total number of students in this group.The research methodology used consisted of two parts relating to 19 issues. The first part is an objective multi choice type of test to measure the student’s skill in selecting the right representation of specific subject graph amongst many provided. The second part concentrated on measuring the student’s skill in construc

The chemical properties of chemical compounds and their molecular structures are intimately connected. Topological indices are numerical values associated with chemical molecular graphs that help in understanding the physicochemical properties, chemical reactivity and biological activity of a chemical compound. This study obtains some topological properties of second and third dominating David derived (DDD) networks and computes several K Banhatti polynomial of second and third type of DDD.

Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph  make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs  of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs  derived from the group  and a few classes of zero-divisor graphs  of the commutative ring R are examined.

The stories of children in Iraq during the past two decades have received a number of important scientific studies. Despite tyranny of the historical study method on most of these studies, they have been and still are very important, because they have established a chronicle of this literary style that has been neglected and based not only on the academic level and serious in-depth university studies but also on the enclosed sight that doesn’t consider studied art as an innovation with its specificity and its typical technical components. While many of the public impressions and self-reflections contributed to the dominance of some of the provisions and concepts that were circulated as critical remarks and adopted by som

Graph  is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree  are determined.