The Vertex Pi and Szeged Indices of an Infinite Family of Fullerenes

Ashrafi, Ali Reza; Ghorbani, Modjtaba; Jalali, M.

doi:10.1142/s0219633608003757

Cited by 52 publications

(47 citation statements)

References 10 publications

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“…Their application in chemistry, biology and nano-science are unlimited. Recently, the topological indices of certain families of dendrimers have been investigated in [9][10][11][12][13][14][15].…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

On Topological Indices of Certain Families of Nanostar Dendrimers

et al. 2016

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Abstract:A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

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Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

On Topological Indices of Certain Families of Nanostar Dendrimers

et al. 2016

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“…Another polynomial also related to the ops in G was introduced by Ashrafi and coauthors [12] in 2008, that counting the non-opposite edges is the Sadhana polynomial Sd(G, x) defined as:…”

Section: K))mentioning

confidence: 99%

On the SD-Polynomial and SD-Index of an Infinite Class of “Armchair Polyhex Nanotubes”

Farahani

2014

ILCPA

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“…Nanobiotechnology is a rapidly advancing area of scientific and technological opportunity that applies the tools and processes of nano-fabrication to build devices for studying bio-systems. Dendrimers are one of the main objects of this new area of science, see [1,[4][5][6][7][8]. Dendrimers are generally synthesized from monomers by iterative growth and activation steps.…”

Section: Introductionmentioning

confidence: 99%

“…They are large and complex, with very well-defined chemical structure, and commercially one of the major available nanoscale building blocks. These are nearly perfect mono-disperse macromolecules with a regular and highly branched three-dimensional architecture [4][5][6]. Their three major architectural components are core, branches and end groups.…”

Section: Introductionmentioning

confidence: 99%

“…New branches emitting from a central core are added in steps until a tree-like structure is formed (see Figures 1-4). Nanostar dendrimer is a part of a new group of macro-particles that appear to be photon funnels just like artificial antennas and are used in the formation of nanotubes, micro and macro-capsules, chemical sensors, colored glasses, and modified electrodes [4,5]. Due to large-scale applications, these compounds are subject matters in both chemistry and mathematics [1,5,6,8].…”

Section: Introductionmentioning

confidence: 99%

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M-Polynomial and Related Topological Indices of Nanostar Dendrimers

et al. 2016

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Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

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The Vertex Pi and Szeged Indices of an Infinite Family of Fullerenes

Abstract: The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. In this paper, the vertex PI and Szeged indices of an infinite family of fullerenes are computed.

Cited by 52 publications

References 10 publications

On Topological Indices of Certain Families of Nanostar Dendrimers

On Topological Indices of Certain Families of Nanostar Dendrimers

On the SD-Polynomial and SD-Index of an Infinite Class of “Armchair Polyhex Nanotubes”

M-Polynomial and Related Topological Indices of Nanostar Dendrimers

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