Relationship between the Hosoya polynomial and the hyper-Wiener index

Cash, Gordon G.

doi:10.1016/s0893-9659(02)00059-9

Cited by 67 publications

(38 citation statements)

References 14 publications

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“…Which was put forward in [7] and since then many research papers are written about this index.For example we can refer the reader to [8], [9] and [10]. We will define the hyperwiener index of a graph as follow …”

Section: The Wiener Index Of Is Denoted Bymentioning

confidence: 99%

The Hyper-Wiener Index of One-pentagonal Carbon Nanocone

Khalifeh¹,

Darafsheh²,

Jolany

2013

CNANO

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Section: The Wiener Index Of Is Denoted Bymentioning

confidence: 99%

The Hyper-Wiener Index of One-pentagonal Carbon Nanocone

Khalifeh¹,

Darafsheh²,

Jolany

2013

CNANO

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“…Higher derivatives of H(G, x) have also been used as descriptors (Konstantinova and Diudea, 2000). From equation (7), hyper-Hosoya polynomial is integrated as (Cash, 2002):…”

Section: Optimal Mathematical Properties Of Bbmentioning

confidence: 99%

Computing optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms

Khataee

Ibrahim

Sourchi

et al. 2012

COMPEL

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Purpose -One of the significant underlying principles of nanorobotic systems deals with the understanding and conceptualization of their respective complex nanocomponents. This paper introduces a new methodology to compute a set of optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms based on dynamic programming and greedy algorithm. Design/methodology/approach -Buckyball, C 60 , is composed of sixty equivalent carbon atoms arranged as a highly symmetric hollow spherical cage in the form of a soccer ball. At first, Wiener, hyper-Wiener, Harary and reciprocal Wiener indices were computed using dynamic programming and presented them as: W(Buckyball) ¼ 11870.4, WW(Buckyball) ¼ 52570.9, Ha(Buckyball) ¼ 102.2 and RW(Buckyball) ¼ 346.9. The polynomials of Buckyball, Hosoya and hyper-Hosoya, which are in relationship with Buckyball's indices, have also been computed. The relationships between Buckyball's indices and polynomials were then computed and demonstrated a good agreement with their mathematical equations. Also, a graph algorithm based on greedy algorithms was used to find some optimal electronic aspects of Buckyball's structure by computing the Minimum Weight Spanning Tree (MWST) of Buckyball. Findings -The computed MWST was indicated that for connecting sixty carbon atoms of Buckyball together: the minimum numbers of double bonds were 30; the minimum numbers of single bonds were 29; and the minimum numbers of electrons were 178. These results also had good agreement with the principles of the authors' used greedy algorithm. Originality/value -This paper has used the graph algorithms for computing the optimal electronic and mathematical properties of BB. It has focused on mathematical properties of BB including Wiener, hyper-Wiener, Harary and reciprocal Wiener indices as well as Hosoya and Hyper-Hosoya polynomials and computerized them with dynamic programming graph algorithms.

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“…For some recent results on the Hosoya polynomial see [5]. What makes the Hosoya polynomial interesting in chemistry is especially the strong connection to the Wiener index and the hyper-Wiener index [2].…”

Section: Introductionmentioning

confidence: 99%

The edge-Hosoya polynomial of benzenoid chains

Tratnik

Pleteršek

2018

J Math Chem

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The Hosoya polynomial is a well known vertex-distance based polynomial, closely correlated to the Wiener index and the hyper-Wiener index, which are widely used molecular-structure descriptors. In the present paper we consider the edge version of the Hosoya polynomial. For a connected graph G let d e (G, k) be the number of (unordered) edge pairs at distance k . Then the edge-Hosoya polynomial of G is H e (G, x) = k≥0 d(G, k) x k . We investigate the edge-Hosoya polynomial of important chemical graphs known as benzenoid chains and derive the recurrence relations for them. These recurrences are then solved for linear benzenoid chains, which are also called polyacenes.

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Relationship between the Hosoya polynomial and the hyper-Wiener index

Cited by 67 publications

References 14 publications

The Hyper-Wiener Index of One-pentagonal Carbon Nanocone

The Hyper-Wiener Index of One-pentagonal Carbon Nanocone

Computing optimal electronic and mathematical properties of Buckyball nanoparticle using graph algorithms

The edge-Hosoya polynomial of benzenoid chains

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