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.
KE Sharquie, SA Al-Meshhadani, AA Al-Nuaimy, Saudi medical journal, 2007 - Cited by 9
This work aims to see the positive association rules and negative association rules in the Apriori algorithm by using cosine correlation analysis. The default and the modified Association Rule Mining algorithm are implemented against the mushroom database to find out the difference of the results. The experimental results showed that the modified Association Rule Mining algorithm could generate negative association rules. The addition of cosine correlation analysis returns a smaller amount of association rules than the amounts of the default Association Rule Mining algorithm. From the top ten association rules, it can be seen that there are different rules between the default and the modified Apriori algorithm. The difference of the obta
... Show MoreIn this paper the proton, neutron and matter density distributions and the corresponding root mean square (rms) radii of the ground states and the elastic magnetic electron scattering form factors and the magnetic dipole moments have been calculated for exotic nucleus of potassium isotopes K (A= 42, 43, 45, 47) based on the shell model using effective W0 interaction. The single-particle wave functions of harmonic-oscillator (HO) potential are used with the oscillator parameters b. According to this interaction, the valence nucleons are asummed to move in the d3f7 model space. The elastic magnetic electron scattering of the exotic nuclei 42K (J?T= 2- 2), 43K(J?T=3/2+ 5/2), 45K (J?T= 3/2+ 7/2) and 47K (J?T= 1/2+ 9/2) investigated t
... Show MoreNasiriya field is located about 38 Km to the north – west of Nasiriya city. Yammama, a giant lower cretaceous reservoir in Nasiriya field which is lithologically formed from limestone. Yammama mainly was divided into three main reservoir units YA, YB1, YB2 and YB3 and it is separated by impermeable layers of variable thickness. An accurate petro physical evolution of the reservoir is of great importance perform an excellent geological model so that four petro physical properties which are shale volume, porosity, water saturation and permeability was re-evaluated. The volume of shale was calculated using the density and neutron logs (VSH-DN) rather than using gamma ray log because of presence a uranium content in the formation that make
... Show MoreIt is well known that the spread of cancer or tumor growth increases in polluted environments. In this paper, the dynamic behavior of the cancer model in the polluted environment is studied taking into consideration the delay in clearance of the environment from their contamination. The set of differential equations that simulates this epidemic model is formulated. The existence, uniqueness, and the bound of the solution are discussed. The local and global stability conditions of disease-free and endemic equilibrium points are investigated. The occurrence of the Hopf bifurcation around the endemic equilibrium point is proved. The stability and direction of the periodic dynamics are studied. Finally, the paper is ended with a numerical simul
... Show MoreAvery large numbers of articles are made by powder metallurgical methods using electrolytically reduced metal powders. Iron powder is one of these powders which play an important role in this field. Its preparation by electrolytic method is economic in comparison with the traditional methods (Atomization and carbonyl processes).
An electrochemical cell consisting of two electrodes (stainless steel cathode and iron anode, 99.9%) was used to study the electrolytic preparation of iron powder with particle size less than 106µm directly as powde1y form. Ferrous sulphate electrolyte was used containing sodium chloride as a stabilizing agent. The produced powder was thoroughly washed with an acidified distilled water and absolute ethan
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