Chemical Graph Theory and the Sherlock Holmes Principle

Hyle 19 (1):107 - 134 (2013)
  Copy   BIBTEX

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Twilight graphs.J. C. E. Dekker - 1981 - Journal of Symbolic Logic 46 (3):539-571.
Effective coloration.Dwight R. Bean - 1976 - Journal of Symbolic Logic 41 (2):469-480.
.Jay Zeman - unknown
Reflections about mathematical chemistry.A. T. Balaban - 2005 - Foundations of Chemistry 7 (3):289-306.
Graph structure and monadic second-order logic: a language-theoretic approach.B. Courcelle - 2012 - New York: Cambridge University Press. Edited by Joost Engelfriet.
Dangerous Reference Graphs and Semantic Paradoxes.Landon Rabern, Brian Rabern & Matthew Macauley - 2013 - Journal of Philosophical Logic 42 (5):727-765.

Analytics

Added to PP
2013-09-11

Downloads
30 (#459,346)

6 months
1 (#1,040,386)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references