Planar rearrangements of fullerenes

A notion of planar rearrangement of fullerenes is proposed as a general framework for all conceivable rearrangements of fullerenes satisfying a minimum physicochemical condition. The planar rearrangement is defined as an edge relocation such that the planarity of a given Schlegel diagram remains undisturbed. Graph-theoretical properties of planar rearrangements are discussed and characteristics for establishing a hierarchy between them are pointed out. A number of graph-theoretical concepts have been introduced to provide means for classification and systematic generation of fullerene rearrangements. The simpliest nontrivial rearrangements is shown to be the Stone-Wales rearrangement.