Topological coordinates for bar polyhex carbon structures
Very often, the basic information about a nanostructure is a topological one. Based on this topological information, we have to determine the Descartes coordinates of the atoms. In the present paper, we review fi rst the previous results obtained by drawing graphs with the help of various matrices as the adjacency matrix, the Laplacian matrix and the Colin de Verdière matrix. We explain why they are applicable if the atoms are on spherical surfaces. We have found recently a matrix W which could generate the Descartes coordinates for fullerenes, nanotubes and nanotori and also for nanotube junctions and coils as well. Here will be shown with examples of bar polyhex structures that using the matrix elements of smaller structures, the W matrix of larger structures can be generated.
KeywordsDrawing Eigenvectors Embedding Graphs Molecular structures Nanostructures
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