Let be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset is a minimum neighborhood dominating set if is a dominating set and if for every holds. The minimum cardinality of the minimum neighborhood dominating set of a graph is called as minimum neighborhood dominating number and it is denoted by . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the smallest number of vertices needed to form a minimum neighborhood-dominating set. The concept of minimum neighborhood dominating set is related to the study of the structure and properties of graphs and is used in various fields such as computer science, operations research, and network design. A minimum neighborhood dominating set is also useful in the study of graph theory and has applications in areas such as network design and control theory. This concept is a variation of the traditional dominating set problem and adds an extra constraint on the intersection of the neighborhoods of the vertices in the set. It is also an NP-hard problem. The main aim of this paper is to study the minimum neighborhood domination number of the split graph of some of the graphs.
One of the most important enhanced oil recoveries methods is miscible displacement. During this method preferably access to the conditions of miscibility to improve the extraction process and the most important factor in these conditions is miscibility pressure. This study focused on establishing a suitable correlation to calculate the minimum miscibility pressure (MMP) required for injecting hydrocarbon gases into southern Iraq oil reservoir. MMPs were estimated for thirty oil samples from southern Iraqi oil fields by using modified Peng and Robinson equation of state. The obtained PVT reports properties were used for tunning the equation of state parameters by making a match between the equation of state results with experimenta
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The goal of the research is to diagnose some of the negative phenomena which was discovered through the period from (2010 to 2014) as determined by the national strategy to eliminate the corruption which was set out by the joint council of the corruption elimination in Iraq. And to measure the gap in applying the legal rules by the administration, concerning the misconducts and felonies upon the state employments made by the state employee and how far they are applied in the studied sample and to show the nature of the rules and their importance and their role when they are applied in scientific and expertise manner. And to encourage the offices of the general supervisors to adhere to them which will lead t
... Show MoreThis paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.
In this work, a deep computational study has been conducted to assign several qualities for the graph . Furthermore, determine the amount of the dihedral subgroups in the Held simple group He through utilizing the attributes of gamma.
The research emphasizes importance of preliminary drawings in design of any product. Therefore, using of simulation as tools for visual thinking in developing drawing and design skills. So that practice of drawing by hand, considering shape of ideas in first stage of visualizations, and practice of its techniques and continuous training.
Hence, the research problem arose with the role of simulation method for developing preliminary sketches in the sample of students of the Product Design Department at the College of Design and Art, PNU, as it is important tool for visual thinking that helps the designer in designing and producing innovative artistic works.
Therefore, the research axes, a number of findings and recommendations were
Let G be a finite group, the result is the involution graph of G, which is an undirected simple graph denoted by the group G as the vertex set and x, y ∈ G adjacent if xy and (xy)2 = 1. In this article, we investigate certain properties of G, the Leech lattice groups HS and McL. The study involves calculating the diameter, the radius, and the girth of ΓGRI.
In this research, the seasonal Optimal Reliable Frequency (ORF) variations between different transmitter/receiver stations have been determined. Mosul, Baghdad, and Basra have been chosen as tested transmitting stations that located in the northern, center, and southern of Iraqi zone. In this research, the minimum and maximum years (2009 and 2014) of solar cycle 24 have been chosen to examine the effect of solar activity on the determined seasonal ORF parameter. Mathematical model has been proposed which leads to generate the Optimal Reliable Frequency that can maintain the seasonal connection links for different path lengths and bearings. The suggested ORF parameter represented by a different orders polynomial equation. The polynom
... Show MoreNearly, in the middle of 1970s the split-brain theory became the only theory that explains human creativity used in all fine art and art education schools. In fact, this theory- which appeared for first time in the middle of 1940s – faced many radical changes including its concepts and structures, and these changes affected both teaching art and art criticism. To update people awareness within art field of study, this paper reviews the split-brain theory and its relationship with teaching art from its appearance to its decay in 2013 and after.