## Abstract

Mathematical chemistry or more accurately discrete mathematical chemistry had a tremendous growth spurt in the second half of the twentieth century and the same trend is continuing in the twenty first century. This continual growth was fueled primarily by two major factors: 1) Novel applications of discrete mathematical concepts to chemical and biological systems, and 2) Availability of high speed computers and relevant software whereby hypothesis driven as well as discovery oriented research on large data sets could be carried out. This led to the development of not only a plethora of new concepts, but also to various useful applications. This chapter will discuss the major milestones in the development of hierarchical QSARs for the prediction of physical as well as biological properties of various classes of chemicals by the Basak group of researchers using mathematical descriptors and different statistical methods.

Original language | English (US) |
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Title of host publication | Advances in Mathematical Chemistry and Applications |

Subtitle of host publication | Revised Edition |

Publisher | Elsevier Inc. |

Pages | 251-281 |

Number of pages | 31 |

Volume | 1 |

ISBN (Electronic) | 9781681081977 |

ISBN (Print) | 9781681081984 |

DOIs | |

State | Published - 2015 |

### Bibliographical note

Funding Information:Subhash C. Basak deeply appreciates the help that he received from the co-editor of this eBook, Guillermo Restrepo. Basak would also like to thank Gregory Grunwald for sustained collaboration and technical support for almost three decades of Basak's research at the University of Minnesota Duluth. Research of SM is supported by the United States National Science Foundation grant IIS-1029711.

Publisher Copyright:

© 2015 Bentham Science Publishers Ltd Published by Elsevier Inc. All rights reserved.

Copyright:

Copyright 2020 Elsevier B.V., All rights reserved.

## Keywords

- Adjacency matrix
- Big data
- Congenericity principle
- Connectivity indices
- Distance matrix
- Diversity begets diversity principle
- E-state indices
- Envelope models
- Graph theoretic matrices
- Graph theory
- Hierarchical quantitative structure-activity relationship (HiQSAR)
- Information theoretic indices
- Interrelated two-way clustering
- Leave one out (LOO) method
- Linear discriminant analysis
- Molecular graphs
- Mutagenicity
- Naïve q
- Partial least square (PLS)
- Principal components analysis (PCA)
- Principal components regression (PCR)
- Proper cross validation
- Property-activity relationship (PAR)
- Quantum chemical descriptors
- Ridge regression (RR)
- Topochemical indices
- Topological indices
- Topostructural indices
- True q
- Valence connectivity indices
- Weighted pseudograph