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Gráfica vista en clase, sus matrices A, B, C y D y la relación entre ellas
"Circuito grande con STA.nb" utiliza el formato ralo (SparseArray), y las instrucciones de gráficas de Mathematica (IncidenceMatrx).
Para correrlo, poner en el mismo directorio (p.ej. Descargas) con los archivos "Spice" de abajo. Se puede escoger cualquiera de estos archivos. El circuito11.txt, que es el más grande, con una matriz normal de 1066x1066, corrió con números reales en 0.0107 seg en una MacBook Pro, mientras que con racionales corrió en 3.81 seg.
Circuito con gráficas y Solve.nb
Referencias
Introductoria
Computer Aided Analysis of Electronic Networks Lecture 2 Ohio University
Tableau Analysis for Resistive Circuits
Artículos pioneros de la teoría de los circuitos
The Sparse Tableau Approach to Network Analysis and Design (1971)
Algorithms for ASTAP-A Network Analysis Program (1973)
Otras aplicaciones de la Teoría de Gráficas
Teoría de gráficas en minería de datos
Chemical Graph Theory (Enlace a Wikipedia)
Chemical graph theory
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena.[1] The pioneers of the chemical graph theory are Alexandru Balaban, Ante Graovac, Ivan Gutman, Haruo Hosoya, Milan Randićand Nenad Trinajstić[2] (also Harry Wiener and others). In 1988, it was reported that several hundred researchers worked in this area producing about 500 articles annually. A number of monographs have been written in the area, including the two-volume comprehensive text by Trinajstic, Chemical Graph Theory, that summarized the field up to mid-1980s.[3]
The adherents of the theory maintain that the properties of a chemical graph (i.e., a graph-theoretical representation of a molecule) give valuable insights into the chemical phenomena. The opponents contend that graphs play only a fringe role in chemical research.[4] One variant of the theory is the representation of materials as infinite Euclidean graphs, particularly crystals by periodic graphs.
Periodic graph (crystallography)
Periodic graph
In crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes are points in three-dimensional Euclidean space, and whose edges (or bonds or spacers) are line segments connecting pairs of vertices, periodic in three linearly independent axial directions.
Applications of Graph Theory in Chemistry (J. Chem. InJ Comput. Sci. 1985, 25, 334-343)
Applications of Graph Theory in Chemistry
Graph theoretical (GT) applications in chemistry underwent a dramatic revival lately. Constitutional (molecular) graphs have points (vertices) representing atoms and lines (edges) symbolizing malent bonds. This review deals with definition. enumeration. and systematic coding or nomenclature of constitutional or steric isomers, valence isomers (especially of annulenes). and condensed polycyclic aromatic hydrocarbons. A few key applications of graph theory in theoretical chemistry are pointed out. The complete set of all poasible monocyclic aromatic and heteroaromatic compounds may be explored by a mmbination of Pauli's principle, P6lya's theorem. and electronegativities. Topological indica and some of their applications are reviewed. Reaction graphs and synthon graphs differ from constitutional graphs in their meaning of vertices and edges and find other kinds of chemical applications. This paper ends with a review of the use of GT applications for chemical nomenclature (nodal nomenclature and related areas), coding. and information processing/storage/retrieval
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