Topological Invariants of Nanocones and Fullerenes

Author(s): Fatemeh Koorepazan-Moftakhar, Ali R. Ashrafi, Ottorino Ori, Mihai V. Putz

Journal Name: Current Organic Chemistry

Volume 19 , Issue 3 , 2015


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Abstract:

The Timisoara-eccentricity (TM-EC) index of a molecular graph  is defined as the sum of δiεiζi over all atoms i in Γ, where ζi, εi and ζi are the degree, eccentricity and the number of atoms at distance εi from atom i. The topological efficiency index of ζ is defined as ρ = 2W / Nw , where W denotes the Wiener index, w is the minimal vertex contribution and N is the number of carbon atoms. This paper is devoted to the study of nanocones and fullerenes by these new graph invariants. It is proved that the TM-EC index of a fullerene ζ can be bounded by a polynomial of degree 2, for twelve infinite series of fullerenes. It is also shown that in one pentagonal carbon nanocone with exactly 5n2 + 10n + 5 carbon atoms, we have ρ ≈ 1.24 and TM - EC = 280n>sup>3 + 385n2 + 195n + 40. Finally, we examine the dual of this nanocone and prove that we have ρ ≈ 1.24 and TM - EC = 70n3 + 20n2 - 5n.

Keywords: Eccentric connectivity index, fullerene, nanocone, TM-eccentricity index, topological efficiency index.

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Article Details

VOLUME: 19
ISSUE: 3
Year: 2015
Published on: 12 March, 2015
Page: [240 - 248]
Pages: 9
DOI: 10.2174/1385272819666141216230152
Price: $65

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