In this article, the ant colony method is utilized for topology optimization of space structures. Strain energy of the structure is minimized while the material volume is limited to a certain amount. In other words, the stiffest possible structure is sought when certain given materials are used. In addition, a noise cleaning technique is addressed to prevent undesirable members in optimum topol...

In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube,...

the n-(2-benzoyl-phenyl) oxalyl derivatives are important models for studying of three-centered intramolecular hydrogen bonding in organic molecules. the quantum theoretical calculations for two crystal structures of n-(2-benzoyl-phenyl) oxalyl (compounds i and ii) were performed by density functional theory (b3lyp method and 6-311+g* basis set). from the optimized structures, geometric paramet...

Abstract: A graph structure is a generalization of simple graphs. Graph structures are very useful tools for the study of different domains of computational intelligence and computer science. In this research paper, we introduce certain notions of intuitionistic neutrosophic graph structures. We illustrate these notions by several examples. We investigate some related properties of intuitionist...

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. A bipolar fuzzy graph structure is a generalization of a bipolar fuzzy graph. In this paper, we present several different types of operations, including composition, Cartesian product, strong product, cross product, and lexicographic product on ...

The most important lattices in Euclidean space of dimension n ≤ 8 are the lattices A n (n ≥ 2 ), D n (n ≥ 4 ), E n (n = 6 , 7 , 8 ) and their duals. In this paper we determine the cell structures of all these lattices and their Voronoi and Delaunay polytopes in a uniform manner. The results for E6 ∗ and E7 ∗ simplify recent work of Worley, and also provide what may be new space-filling polytope...