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.
The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.
The Asphalt cement is produced as a by-product from the oil industry; the asphalt must practice further processing to control the percentage of its different ingredients so that it will be suitable for paving process. The objective of this work is to prepare different types of modified Asphalt cement using locally available additives, and subjecting the prepared modified Asphalt cement to testing procedures usually adopted for Asphalt cement, and compare the test results with the specification requirements for the modified Asphalt cement to fulfill the paving process requirements. An attempt was made to prepare the modified Asphalt cement for pavement construction in the laboratory by digesting each of the two penetration grade Asphalt c
... Show MoreThe research focuses,in the first place, on six fields.The most important one is
curriculum field which includes the revision of the current academic curriculums and
substitute them with recent ones, beside the rehabilitation of academic labs and factories by
providing them with modern scientific technologies employed in the world. Regarding the
economical field, it seeks to provide high-level training staffs to serve different social and
economical sectors through modern effective technological and scientific
curriculums.Whereas the social field assures the concern of different social classes who
deprived from the grace of higher education such as retirees and elderly people and to set-up
some educational and ent
The main object of this paper is to study the representations of monomial groups and characters technique for representations of monomial groups. We refer to monomial groups by M-groups. Moreover we investigate the relation of monomial groups and solvable groups. Many applications have been given the symbol G e.g. group of order 297 is an M-group and solvable. For any group G, the factor group G/G? (G? is the derived subgroup of G) is an M-group in particular if G = Sn, SL(4,R).
Electronic spectra and kinetic studies of the hydrolysis of trans complexes where fernet acidic media,where carried out fairly
This research deals with the most important grammatical views of the science of the media of the Arab and Andalusian grammar is: Abu Ali al-Shloubini, who filled his name the pages of important grammatical books such as: (singer Al-Labib) Ibn Ibn Hisham, and the book (like and analogues), and (Hama Alhwama) for Suyuti, and other books The task, I have divided my research into the topics: I talked in the first section on his life and his biography and his works, and the second topic: it included his independent opinions and the third section contained the most prominent views selected The fourth and final topic, was his responses to grammarians, and concluded my research with the most prominent findings Research to them, which was the mos
... Show MoreMany studies have focused on identifying and classifying freshwater fishes in Iraq, concerned with describing, organizing, and drawing up a list of freshwater fishes in Iraq or the Tigris and Euphrates rivers. Within the most recent updates at the beginning of 2023, 53 native freshwater and 20 exotic (alien or introduced) fish species are recorded and described. This study reviewed the database of morphology and molecular studies of freshwater fish in Iraq and reported species while surveying the fish fauna at different water bodies of the country from 2010 to the beginning of 2023. In conclusion, 29 species (about 40.3%) of all 72 fish species in Iraq still need to be available information on their molecular data.