EQUIVALENCE OF MATHEMATICAL OBJECTS OF INTEREST IN CHEMISTRY AND PHYSICS

We review various aspects of equivalence relations occuring in chemistry and physics which are of potential interest to chemists. In particular we illustrate various equivalences that yield alternative representation of a same problem or that lead to novel insights. The review focuses on the use of graphical graph invariants as well as graph codes, graph algorithms, and graph characterizations to illustrate: How viewing “old things from a new point of view” may lead to novel results, how old results can be obtained in a simpler way, how novel concepts emerge, and how hidden results become apparent- The review is divided into three parts, the first gives a general overview of the subject, while the second part considers a particular application to benzenoid compounds illustrating data reduction aspects of use for equivalences The third part deals with the fractal dimensions of graphs and correlation with physical properties “The formulation is mathematically equivalent to more usual formulations- There are therefore, no fundamentally new results However, there is a pleasure in recognizing old things from a new point of view”. © 1992, Elsevier Inc. All rights reserved.