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GraphDrawing Algorithms Geometries Versus Molecular Mechanics in Fullerenes
, 1996
"... The algorithms of KamadaKawai (KK) and FruchtermanReingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283.) in order to draw molecular graphs in threedimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular ..."
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Cited by 3 (2 self)
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The algorithms of KamadaKawai (KK) and FruchtermanReingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283.) in order to draw molecular graphs in threedimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries.
Generating Fullerenes at Random
, 1996
"... In the present paper a method for generating fullerenes at random is presented. It is based on the well known StoneWales (SW) transformation. The method could be further generalised so that other trivalent polyhedra with prescribed properties are generated. 1. INTRODUCTION Fullerenes and other pu ..."
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Cited by 2 (2 self)
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In the present paper a method for generating fullerenes at random is presented. It is based on the well known StoneWales (SW) transformation. The method could be further generalised so that other trivalent polyhedra with prescribed properties are generated. 1. INTRODUCTION Fullerenes and other pure carbon cages remain a subject of rigorous research. The mechanism of fullerenes growth is still not fully understood although much has been learned 1 . In the present paper a method for generating fullerenes at random is presented. It is based on the well known StoneWales (SW) transformation 2; 3 and it has been successfully implemented as a part of the VEGA: a system for manipulating discrete mathematical structures. 4; 5 The method could be further generalised so that it is able to narrow the population of carbon cages with special properties. From a mathematical standpoint a fullerene is planar trivalent graph whose faces are pentagons and hexagons. It turns out that the number...
Isoperimetric Quotient for Fullerenes and Other Polyhedral Cages
"... The notion of Isoperimetric Quotient (IQ) of a polyhedron has been already introduced by Polya. It is a measure that tells us how spherical is a given polyhedron. If we are given a polyhedral graph it can be drawn in a variety of ways in 3D space. As the coordinates of vertices belonging to the same ..."
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The notion of Isoperimetric Quotient (IQ) of a polyhedron has been already introduced by Polya. It is a measure that tells us how spherical is a given polyhedron. If we are given a polyhedral graph it can be drawn in a variety of ways in 3D space. As the coordinates of vertices belonging to the same face may not be coplanar the usual definition of IQ fails. Therefore, a method based on a proper triangulation (obtained from omnicapping) is developed that enables to extend the definition of IQ and compute it for any 3D drawing. The IQ's of fullerenes and other polyhedral cages are computed and compared for their NiceGraph and standard Laplacian 3D drawings. It is shown that the drawings with the maximal IQ values reproduce well the molecular mechanics geometries in the case of fullerenes and exact geometries for Platonic and Archimedean polyhedra.
Evolutionary Algorithms for Cluster Geometry
"... The paper presents a genetic algorithm for maximizing the Isoperimetric Quotient of polyhedral clusters. This algorithm helped extending the definition of Isoperimetric Quotient to clusters with nonplanar faces. Detailed description of the genetic algorithm is followed by the performance analysis. S ..."
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The paper presents a genetic algorithm for maximizing the Isoperimetric Quotient of polyhedral clusters. This algorithm helped extending the definition of Isoperimetric Quotient to clusters with nonplanar faces. Detailed description of the genetic algorithm is followed by the performance analysis. Some other observations of genetic algorithm's behavior are also presented.
An Algorithm for Drawing Schlegel Diagrams
, 1996
"... this paper a simple algorithm for drawing Schlegel diagrams is presented. It is derived from the Fruchterman and Reingold spring embedding algorithm by deleting all repulsive forces and fixing vertices of an outer face. The algorithm is implemented in the system for manipulating discrete mathematica ..."
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this paper a simple algorithm for drawing Schlegel diagrams is presented. It is derived from the Fruchterman and Reingold spring embedding algorithm by deleting all repulsive forces and fixing vertices of an outer face. The algorithm is implemented in the system for manipulating discrete mathematical structures Vega. Some examples of derived figures are given.