This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermore, providing the necessary condition for α-feebly normality property to become hereditary. Also, using a new topological model for graphs are the edges represented as points which enables us to express in a topological language about combinatorial concepts. Moreover, showing that an α-connected orderable spaces are exactly α-topologized graphs. Finally, realizing the relationship between the α-topology on the vertex set and the once on the whole space by α-feebly regularity property.
In this paper, a new type of supra closed sets is introduced which we called supra β*-closed sets in a supra topological space. A new set of separation axioms is defined, and its many properties are examined. The relationships between supra β*-Ti –spaces (i = 0, 1, 2) are studied and shown with instances. Additionally, new varieties of supra β*-continuous maps have been taken into consideration based on the supra β*-open sets theory.
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Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.
In the present paper, we have introduced some new definitions On D- compact topological group and D-L. compact topological group for the compactification in topological spaces and groups, we obtain some results related to D- compact topological group and D-L. compact topological group.
The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.
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Assume that G is a finite group and X = tG where t is non-identity element with t3 = 1. The simple graph with node set being X such that a, b ∈ X, are adjacent if ab-1 is an involution element, is called the A4-graph, and designated by A4(G, X). In this article, the construction of A4(G, X) is analyzed for G is the twisted group of Lie type 3D4(3).
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
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Our country suffered from pollution translation as a result to the wars events, so, it is necessary to measure the amount of radiation in the fields that are of indirect contact with human life and health. The main aim of the present work is to measure the concentration of alpha emitters in tomato fruits collected from different farms in Al – Basra governorate in the south of Iraq. Nuclear track detectors of type CR – 39 are used as a detection device and Can technique as a detection technique. Results show that the maximum concentration recorded is sample no.7 of site Al – Rafidhya which was equal to (6.9621 ± 0.111) ppm and sample no.1 of site Lothan with concentration equals to (4.9236 ± 0.117) ppm. The minimum concentratio
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The Gaussian orthogonal ensemble (GOE) version of the random matrix theory (RMT) has been used to study the level density following up the proton interaction with 44Ca, 48Ti and 56Fe.
A promising analysis method has been implemented based on the available data of the resonance spacing, where widths are associated with Porter Thomas distribution. The calculated level density for the compound nuclei 45Sc,49Vand 57Co shows a parity and spin dependence, where for Sc a discrepancy in level density distinguished from this analysis probably due to the spin misassignment .The present results show an acceptable agreement with the combinatorial method of level density.
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