On sublinks and their connections within the graphs of the mechanically bound molecules

Abstract

The concept of sublinks has been further developed and has been used in the new form for the analysis of the graphs of complex mechanically bound molecules. This analysis is additionally supported by the Brunnian numbers M, μ for topologically non-trivial and their complements L and λ for topologically trivial systems (like [n]-rotaxanes). The detailed topological analysis has been thus performed for more than thirty topologically different structures. The different orders of (sub)links, single and multiple mechanical bonds ought to be discerned to analyze connections within the larger structures. The new nomenclature recommendations developed suggest to indicate the number of the mechanical bonds, their (highest) multiplicities together with the number of covalent units and the number of interlocked rings or rings and dumbbells.