Article ID: CBB001320764

Chemical Graph Theory and the Sherlock Holmes Principle (2013)


Abstract: The development of chemical applications of graph theory is reviewed from a personal perspective. Graph-theoretical methods for finding all graphs fulfilling certain mathematical conditions followed by eliminating chemically impossible solutions are equivalent to the `Sherlock Holmes principle'. For molecular graphs, this is illustrated by monocyclic aromatic systems and by valence isomers of annulenes. Using dualist graphs for benzenoids and diamond hydrocarbons it was possible to develop simple encoding systems that allowed convenient enumerations of isomers. Starting with the invention of reaction graphs in 1966 that included the Petersen graph which is also the 5-cage (the smallest graph with girth 5) two gaps were filled by discovering the first 10-cage and the unique 11-cage, showing how chemical clues can lead to interesting mathematical developments. Graphs of a third type are represented by synthon graphs that are helping chemical synthesis. Connections between chemical structure and molecular properties allow the design of biologically active substances on the basis of quantitative structure-activity relationships (QSARs). Some of the simplest tools for QSAR are topological indices and they are briefly discussed. Keywords: mathematical chemistry, molecular graphs, reaction graphs, synthon graphs, topological indices, QSAR.


Description Looks at the ways in which the use of mathematical chemistry has contributed to discoveries in the respective fields.

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Authors & Contributors
Restrepo, Guillermo
Villaveces, José L.
De Berg, Kevin
Steingart, Alma
Yuan, Yuan
Wright, Aaron Sidney
Science and Education
British Society for the History of Mathematics Bulletin
Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences
Statistical Science
Springer International
Massachusetts Institute of Technology, MIT
Mathematics and its relationship to science
Applied mathematics
Visual representation; visual communication
Wigner, Eugene Paul
Pauling, Linus Carl
Wiener, Norbert
Wheland, George Willard
Sylvester, James Joseph
Time Periods
20th century, late
20th century
19th century
21st century
United States
Eastern Europe
Great Britain
Massachusetts Institute of Technology, MIT

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