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 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 Trinajstić, 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. Others 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.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc.
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. Finding a matching in a bipartite graph can be treated as a network flow problem.
Johann Josef Loschmidt, who referred to himself mostly as Josef Loschmidt, was a notable Austrian scientist who performed ground-breaking work in chemistry, physics, and crystal forms.
Chemical physics is a subdiscipline of chemistry and physics that investigates physicochemical phenomena using techniques from atomic and molecular physics and condensed matter physics; it is the branch of physics that studies chemical processes from the point of view of physics. While at the interface of physics and chemistry, chemical physics is distinct from physical chemistry in that it focuses more on the characteristic elements and theories of physics. Meanwhile, physical chemistry studies the physical nature of chemistry. Nonetheless, the distinction between the two fields is vague, and scientists often practice in both fields during the course of their research.
Mathematical chemistry is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. Mathematical chemistry has also sometimes been called computer chemistry, but should not be confused with computational chemistry.
Jaroslav (Jarik) Nešetřil is a Czech mathematician, working at Charles University in Prague. His research areas include combinatorics, graph theory, algebra, posets, computer science.
The Hosoya index, also known as the Z index, of a graph is the total number of matchings in it. The Hosoya index is always at least one, because the empty set of edges is counted as a matching for this purpose. Equivalently, the Hosoya index is the number of non-empty matchings plus one. The index is named after Haruo Hosoya.
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. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure.
In chemical graph theory, the Wiener index 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.
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 with the kinds of the corresponding atoms and edges are labeled with the types of bonds. For particular purposes any of the labelings may be ignored.
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
Milan Randić is a Croatian American scientist who is one of the leading experts in the field of computational chemistry.
In the mathematical fields of graph theory and combinatorics, a matching polynomial is a generating function of the numbers of matchings of various sizes in a graph. It is one of several graph polynomials studied in algebraic graph theory.
In graph theory, a caterpillar or caterpillar tree is a tree in which all the vertices are within distance 1 of a central path.
In chemistry, topology provides a way of describing and predicting the molecular structure within the constraints of three-dimensional (3-D) space. Given the determinants of chemical bonding and the chemical properties of the atoms, topology provides a model for explaining how the atoms ethereal wave functions must fit together. Molecular topology is a part of mathematical chemistry dealing with the algebraic description of chemical compounds so allowing a unique and easy characterization of them.
In mathematics, the energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. This quantity is studied in the context of spectral graph theory.
Ante Graovac is a Croatian scientist known for his contribution to chemical graph theory. He was director of 26 successful annual meetings MATH/CHEM/COMP held in Dubrovnik. He was Secretary of the International Academy of Mathematical Chemistry.
Nenad Trinajstić is a Croatian chemist and one of pioneers of the chemical graph theory.
Iván Gutman is a Serbian chemist and mathematician.