Topological Efficiency of Fullerene

چکیده مقاله

The topological efficiency index of a fullerene F is defined as ho=2W/Nunderline{w}, where W denotes the Wiener index of F, underline{w} is minimal vertex contribution and N is the number of carbon atoms. It is shown that in two infinite families of fullerenes with exactly 12(2n+1) and 12n+8 carbon atoms, we have 1≤ ho<4/3. We also proved that for any natural number n, there are infinite number of fullerenes with 4/3− ho<10^{−n} .