Combination of distance and symmetry in some molecular graphs

Koorepazan-Moftakhar, Fatemeh; Ashrafi, Ali Reza

doi:10.1016/j.amc.2016.01.065

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…[4] On one side, the mathematical properties of the Graovac-Pisanski index were investigated. For example, the index was intensely studied for nanostructures, [5][6][7][8][9][10] some general results on the Graovac-Pisanski index were obtained, [11,12] the closed formulae for carbon nanotubes were calculated, [13,14] extremal trees were considered, [15] and the symmetries of molecules were studied. [16,17] On the other side, the chemical usefulness of the Graovac-Pisanski index was shown in, [18] where the connection with the topological efficiency was considered and later in, [19] where the correlation with the melting points of some families of hydrocarbon molecules was established.…”

Section: Introductionmentioning

confidence: 99%

The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon molecules

Črepnjak

Knor

Tratnik

et al. 2021

Fullerenes, Nanotubes and Carbon Nanostructures

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The Graovac-Pisanski index, also called the modified Wiener index, was introduced in 1991 and represents an extension of the original Wiener index, because it considers beside the distances in a graph also its symmetries. Similarly as Wiener in 1947 showed the correlation of the Wiener indices of the alkane series with the boiling points, in 2018 the connection between the Graovac-Pisanski index and the melting points of some hydrocarbon molecules was established. In this paper, we prove that the Graovac-Pisanski index of any connected bipartite graph as well as of any connected graph on an even number of vertices is an integer number. These results are applied to some important families of hydrocarbon molecules. By using a computer programme, the graphs with a non-integer Graovac-Pisanski index on at most nine vertices are counted. Finally, an infinite class of unicyclic graphs with a non-integer Graovac-Pisanski index is described.

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Section: Introductionmentioning

confidence: 99%

The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon molecules

Črepnjak

Knor

Tratnik

et al. 2021

Fullerenes, Nanotubes and Carbon Nanostructures

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“…This difference was computed in [9] for some families of polyhedral graphs. The Graovac-Pisanski index of nanostructures was studied in [1,2,15,16,17] and for some classes of fullerenes and fullerene-like molecules in [3,11,12]. In [13] the symmetry groups and Graovac-Pisanski index of some linear polymers were computed.…”

Section: Introductionmentioning

confidence: 99%

Unicyclic graphs with the maximal value of Graovac-Pisanski index

Knor¹,

Komorník²,

Škrekovski³

et al. 2019

Ars Math. Contemp.

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Let G be a graph and let Γ be its group of automorphisms. Graovac-Pisanski index of G is GP(G) = |V (G)| 2|Γ| u∈V (G) α∈Γ d(u, α(u)), where d(u, v) is the distance from u to v in G. One can observe that GP(G) = 0 if G has no nontrivial automorphisms, but it is not known which graphs attain the maximum value of Graovac-Pisanski index. In this paper we show that among unicyclic graphs on n vertices the n-cycle attains the maximum value of Graovac-Pisanski index.

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“…Very recently, the Graovac-Pisanski index of some molecular graphs and nanostructures was extensively studied 1,3,[7][8][9]13 . Moreover, the closed formulas for the Graovac-Pisanski index of zigzag nanotubes were computed 14 .…”

Section: Introductionmentioning

confidence: 99%

Predicting melting points of hydrocarbons by the Graovac-Pisanski index

Črepnjak

Tratnik

Pleteršek

2018

Fullerenes, Nanotubes and Carbon Nanostructures

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Theoretical molecular descriptors alias topological indices are a convenient means for expressing in a numerical form the chemical structure encoded in a molecular graph. The structure descriptors derived from molecular graphs are widely used in Quantitative Structure-Property Relationship (QSPR) and Quantitative Structure-Activity Relationship (QSAR).In this paper, we are interested in the Graovac-Pisanski index (also called modified Wiener index) introduced in 1991 by Graovac and Pisanski, which encounters beside the distances in a molecular graph also its symmetries. In the QSPR analysis we first calculate the Graovac-Pisanski index for different families of hydrocarbon molecules using a simple program and then we show a correlation with the melting points of considered molecules. We show that the melting points of the alkane series can be very effectively predicted by the Graovac-Pisanski index and for the rest of considered molecules (PAH's and octane isomers) the regression models are different, but we establish some correlation with the melting points for them as well.

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Combination of distance and symmetry in some molecular graphs

Cited by 8 publications

References 6 publications

The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon molecules

The Graovac-Pisanski index of connected bipartite graphs with applications to hydrocarbon molecules

Unicyclic graphs with the maximal value of Graovac-Pisanski index

Predicting melting points of hydrocarbons by the Graovac-Pisanski index

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