Chromatic Polynomials of Certain Polyphenylene Dendrimers

Arif, Nabeel E.; Hasni, Roslan; Alikhani, Saeid

doi:10.1166/jctn.2012.2061

Cited by 7 publications

(9 citation statements)

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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%

“…We first consider the PAMAM dendrimer of generation G n with n growth stages, denoted by PD 1 rns where n ě 0. The number of vertices and edges in PD 1 rns are 12ˆ2 n`2´2 3 and 12ˆ2 n`2´2 4 (see [13]). Denote an edge connecting a vertex i to a vertex j by pi, jq´edge, where n i denote the vertex i and s ij is the number of pi, jq´edges.…”

Section: Resultsmentioning

confidence: 99%

“…(see [13]). Denote an edge connecting a vertex to a vertex by ( , ) −edge, where denote the vertex and is the number of ( , ) −edges.…”

Section: Resultsmentioning

confidence: 99%

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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%

Section: Resultsmentioning

confidence: 99%

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On Topological Indices of Certain Families of Nanostar Dendrimers

et al. 2016

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“…Recently some people investigated the mathematical properties of these nanostructures (see for example [1,2,5,7,8]). …”

Section: Introductionmentioning

confidence: 99%

The neighbourhood polynomial of some families of dendrimers

Husin

Hasni

2018

J. Phys.: Conf. Ser.

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Email: naz_reyhusin@yahoo.com; hroslan@umt.edu.my Abstract.The neighbourhood polynomial is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph and it is defined as , where is neighbourhood complex of a graph, whose vertices of the graph and faces are subsets of vertices that have a common neighbour. A dendrimers is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, we compute this polynomial for some families of dendrimer.

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“…Recently some people investigated the mathematical properties of this nanostructures in Refs. [1,3,4,6,7,12,14,16]. In particular, the eccentric connectivity polynomial of some nanostructures are determined by some people in Refs.…”

Section: Introductionmentioning

confidence: 99%

Eccentric Connectivity Polynomials of Some Families of Dendrimers

Hasni¹,

Arif²,

Alikhani³

2014

Jnl of Comp & Theo Nano

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The eccentric connectivity polynomial of molecular graph G is defined aswhere ecc v is defined as the length of a maximal path connecting to another vertex of G. A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, the eccentric connectivity polynomials of three classes of dendrimers, namely, tetrathiafulvalene, siloxane and polyther are computed.

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Chromatic Polynomials of Certain Polyphenylene Dendrimers

Cited by 7 publications

References 0 publications

On Topological Indices of Certain Families of Nanostar Dendrimers

On Topological Indices of Certain Families of Nanostar Dendrimers

The neighbourhood polynomial of some families of dendrimers

Eccentric Connectivity Polynomials of Some Families of Dendrimers

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