Fullerene graphs are mathematical fashions of fullerene molecules. The Wiener (r,s)-complexity of a fullerene graph G with vertex set V(G) is the variety of pairwise distinct values of (r,s)-transmission
of its vertices v:
for constructive integer r and s. The Wiener (1,1)-complexity is named the Wiener complexity of a graph. Irregular graphs have most complexity equal to the variety of vertices. No irregular fullerene graphs are identified for the Wiener complexity. Fullerene (IPR fullerene) graphs with n vertices having the maximal Wiener (r,s)-complexity are counted for all
) and small r and s. The irregular fullerene graphs are additionally introduced.