On the Wiener (r,s)-complexity of fullerene graphs

Abstract

Fullerene graphs are mathematical models of fullerene molecules. The Wiener (r,s)-complexity of a fullerene graph G with vertex set V(G) is the number of pairwise distinct values of (r,s)-transmission of its vertices v: for positive integer r and s. The Wiener (1,1)-complexity is known as the Wiener complexity of a graph. Irregular graphs have maximum complexity equal to the number of vertices. No irregular fullerene graphs are known 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 also presented.