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On the Wiener complexity and the Wiener index of fullerene graphs
Fullerenes are molecules in the form of cage-like polyhedra, consisting
solely of carbon atoms. Fullerene graphs are mathematical models of fullerene
molecules. The transmission of a vertex of a graph is the sum of distances
from to all the other vertices. The number of different vertex
transmissions is called the Wiener complexity of a graph. Some calculation
results on the Wiener complexity and the Wiener index of fullerene graphs of
order are presented. Structure of graphs with the maximal Wiener
complexity or the maximal Wiener index is discussed and formulas for the Wiener
index of several families of graphs are obtained.Comment: 14 pages, 5 figure