In search of structural invariants

Graph theory has been used for modeling chemical structures, that is, chemical compounds, intermediates, changes, reactions and mechanisms. Among the most important such applications are: (1) structure-property relationships (SAR); (2) design of compounds of desired properties; (3) enumeration and construction of compounds of certain classes; (4) unique representation of compounds (for documentation needs). Here, we outline selected accomplishments of the past, show some current efforts and point to directions which may lead to further advancements in chemical graph theory.Dedicated to Linus Pauling (Nobel Prize for Peace 1962 and Nobel Prize for Chemistry 1954) in appreciation of his outstanding contributions to structural chemistry and his untiring efforts to end war.