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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 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 ...
In graph theory, the degree of a vertex is its number of connections. In a chemical graph, the maximum degree of an atom is its valence, and the maximum number of bonds a chemical element can make. For example, carbon's valence is 4. In a chemical graph, an atom is saturated if it reaches its valence.
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]
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 .
Alexandru T. Balaban (born April 2, 1931 in Timișoara) [1] is a Romanian chemist who made significant contributions to the fields of organic chemistry, theoretical chemistry, mathematical chemistry, and chemical graph theory.
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.
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.