Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry

Abstract

Harary's & Randi's ideas of "forcing" & "freedom" involve subsets of double bonds of Kekule structure such as to be unique to that Kekule structure. Such forcing sets are argued to be greatly generalizable to deal with various other coverings, and thence forcing seems to be fundamental, and of notable potential utility. Various forcing invariants associated to (molecular) graphs ensue, with illustrative (chemical) examples and some mathematical consequences being provided. A complementary "uniqueness" idea is noted, and the general characteristic of "derivativity" of "forcing" is established (as is relevant for QSPR fittings). Different ways in which different sorts of forcings arise in chemistry are briefly indicated.(