Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

We define L-contraction mapping in the setting of D-metric spaces analogous to L-contraction mappings [1] in complete metric spaces. Also, give a definition for general D- matric spaces.And then prove the existence of fixed point for more general class of mappings in generalized D-metric spaces.

Comes interest in the subject matter in the selection of the Family industry globally as one of the important industries which have developed a clear and significant in recent years, to look at these products and designs to their functional importance have appeared in recent years, the phenomenon of the small spaces because of housing Population density showed the need to find a spare Furniture fit these small spaces On this basis, determine the objective of this research is to arrive at a design techniques for dual-family employee for small spaces research sample included a double family manufactured in laboratories industry Furniture in Baghdad and local research sample includes family double Decker.Research focused on the first four c

The concept of Cech fuzzy soft bi-closure space ( ˇ Cfs bi-csp) ( ˇ U, L1, L2, S) is initiated and studied by the authors in [6]. The notion of pairwise fuzzy soft separated sets in Cfs bi-csp is defined in this study, and various features of ˇ this notion are proved. Then, we introduce and investigate the concept of connectedness in both Cfs bi-csps and its ˇ associated fuzzy soft bitopological spaces utilizing the concept of pairwise fuzzy soft separated sets. Furthermore, the concept of pairwise feebly connected is introduced, and the relationship between pairwise connected and pairwise feebly connected is discussed. Finally, we provide various instances to further explain our findings.

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined and studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pairwise pseudo and pairwise Uryshon) - fs bicsp's are introduced and studied in both ech fuzzy soft bi-closure space and their induced fuzzy soft bitopological spaces. It is shown that hereditary property is satisfied for , with respect to ech fuzzy soft bi-closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of ech fuzzy soft bi-closure space.

The theory of general topology view for continuous mappings is general version and is applied for topological graph theory. Separation axioms can be regard as tools for distinguishing objects in information systems. Rough theory is one of map the topology to uncertainty. The aim of this work is to presented graph, continuity, separation properties and rough set to put a new approaches for uncertainty. For the introduce of various levels of approximations, we introduce several levels of continuity and separation axioms on graphs in Gm-closure approximation spaces.

            In this paper the definition of fuzzy anti-normed linear spaces and its basic properties are used to prove some properties of a finite dimensional fuzzy anti-normed linear space.    

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact

The formal integration of the interior spaces in general and the commercial spaces of the watch shops in the large commercial centers in particular is the goal that the designers aim to reach in order for the interior space to become successful in terms of the design idea and its characteristics. Implementation mechanism. One of the reasons for achieving formal integration in the interior spaces of watch shops is the requirements of the design that must be available in these spaces to reach a state of formal integration between the interior and the exterior so that the space becomes fully integrated in all respects. Because of the aforementioned reasons for dealing with the research, through four chapters: The first chapter included the