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In chemical graph theory and in mathematical chemistry, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound in terms of graph theory. A chemical graph is a labeled graph whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. Its vertices are labeled ...
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena. [1] The pioneers of chemical graph theory are Alexandru Balaban, Ante Graovac, Iván Gutman, Haruo Hosoya, Milan Randić and Nenad Trinajstić [2] (also Harry Wiener and others). In 1988, it was ...
In chemical graph theory, the Wiener index (also Wiener number) introduced by Harry Wiener, is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph representing the non-hydrogen atoms in the molecule.
Graph theory is also used to study molecules in chemistry and physics. In condensed matter physics , the three-dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms.
In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. [1]
It is an application of graph theory, specifically subgraph matching in which the query is a hydrogen-depleted molecular graph. The mathematical foundations for the method were laid in the 1870s, when it was suggested that chemical structure drawings were equivalent to graphs with atoms as vertices and bonds as edges.
Mathematical chemistry [1] is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. [2] Mathematical chemistry has also sometimes been called computer chemistry , but should not be confused with computational chemistry .
In chemical graph theory, the Padmakar–Ivan (PI) index is a topological index of a molecule, used in biochemistry.The Padmakar–Ivan index is a generalization introduced by Padmakar V. Khadikar and Iván Gutman [1] of the concept of the Wiener index, introduced by Harry Wiener.