On the Wiener (r,s)-complexity of fullerene graphs: Fullerenes, Nanotubes and Carbon Nanostructures: Vol 0, No 0

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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.


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