The maximum Wiener polarity index of unicyclic graphs

Hou, Huoquan; Liu, Bolian; Huang, Yufei

doi:10.1016/j.amc.2012.03.090

Cited by 27 publications

(19 citation statements)

References 6 publications

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“…Lemma 3 ([62, 67]) Let U = ( V , E ) be a unicyclic graph. Let C denote the unique cycle of U :

If g ( U ) = 3 with V ( C ) = { v 1 , v 2 , v 3 }, then

If g ( U ) = 4 with V ( C ) = { v 1 , v 2 , v 3 , v 4 }, then

If g ( U )≥5, then

…”

Section: Preliminaries and The Square Latticesmentioning

confidence: 99%

“…Later, Deng, Xiao and Tang characterized the extremal trees with respect to this index among all trees of order n and diameter k [61]. While for cycle-containing graphs, the maximum Wiener polarity index of unicyclic graphs and the corresponding extremal graphs were determined in [62]. In [63] Ma et al determined the sharp upper bound of the Wiener polarity index among all bicyclic networks based on some graph transformations.…”

Section: Introductionmentioning

confidence: 99%

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On the Wiener Polarity Index of Lattice Networks

et al. 2016

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Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also known as topological indices, have recently been incorporated as descriptors of complex networks. Among them the Wiener type indices are the most well known and commonly used such descriptors. As one of the fundamental variants of the original Wiener index, the Wiener polarity index has been introduced for a long time and known to be related to the cluster coefficient of networks. In this paper, we consider the value of the Wiener polarity index of lattice networks, a common network structure known for its simplicity and symmetric structure. We first present a simple general formula for computing the Wiener polarity index of any graph. Using this formula, together with the symmetric and recursive topology of lattice networks, we provide explicit formulas of the Wiener polarity index of the square lattices, the hexagonal lattices, the triangular lattices, and the 33 ⋅ 42 lattices. We also comment on potential future research topics.

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“…Lemma 3 ([62, 67]) Let U = ( V , E ) be a unicyclic graph. Let C denote the unique cycle of U :

If g ( U ) = 3 with V ( C ) = { v 1 , v 2 , v 3 }, then

If g ( U ) = 4 with V ( C ) = { v 1 , v 2 , v 3 , v 4 }, then

If g ( U )≥5, then

…”

Section: Preliminaries and The Square Latticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Wiener Polarity Index of Lattice Networks

et al. 2016

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“…Recently, the first three minimum

W_{p}

values of molecular trees were determined in ,. Some results concerning Wiener polarity index of graphs, other than trees, can be found in the papers …”

Section: Introductionmentioning

confidence: 99%

The Alkanes with Maximum Wiener Polarity Index

Ali

2018

Molecular Informatics

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The Wiener polarity index (usually denoted by Wp ) of an alkane is the number of unordered pairs of carbon atoms which are separated by three carbon-carbon bonds. This topological index Wp is useful for predicting the boiling points of alkanes. Deng [MATCH Commun. Math. Comput. Chem. 66 (2011) 305] proved that the maximum Wp value among all alkanes, with n carbon atoms, is 3n-15 . The main purpose of present paper is to find all those alkanes with n carbon atoms, which attain the maximum value of Wp .

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“…In recent years, a lot of research has been done in investigating the Wiener polarity index of trees [12,13] and unicyclic graphs. [14] Also, the Nordhaus-Gaddum-type results for this index were considered. [15,16] Some other recent investigations on the Wiener polarity index include results about fullerene graphs, [17] generalizations of the Wiener polarity index, [18] and algorithms.…”

Section: Introductionmentioning

confidence: 99%

The Wiener Polarity Index of Benzenoid Systems and Nanotubes

Tratnik

2018

Croat. Chem. Acta

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In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry, materials engineering, and in drug design since they can be correlated with a large number of physico-chemical properties of molecules. As the main result, we develop a method for computing the Wiener polarity index for two basic and most commonly studied families of molecular graphs, benzenoid systems and carbon nanotubes. The obtained method is then used to find a closed formula for the Wiener polarity index of any benzenoid system. Moreover, we also compute this index for zig-zag and armchair nanotubes.

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The maximum Wiener polarity index of unicyclic graphs

Cited by 27 publications

References 6 publications

On the Wiener Polarity Index of Lattice Networks

On the Wiener Polarity Index of Lattice Networks

The Alkanes with Maximum Wiener Polarity Index

The Wiener Polarity Index of Benzenoid Systems and Nanotubes

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