Combinatorial models and algorithms in chemistry. The expanded Wiener number—a novel topological index

Tratch, Serge S.; Stankevitch, M. I.; Зефиров, Н. С.

doi:10.1002/jcc.540110802

Cited by 75 publications

(55 citation statements)

References 23 publications

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“…The connectivity index is a measure of the branching of hydrocarbons, and the generalized valence connectivity index is a generalised version that can handle heteroatoms [12]. The first descriptor based on conformation is the radius of gyration (rg), a measure of the conformational size of a macromolecule [23], the root square sum of all the distances from the atoms to the centre of the molecule r0, where the centre is given by Sketches of conformations, case A: saturated parallel, B: unsaturated "parallel", C: unsaturated folded.…”

Section: Molecular Descriptorsmentioning

confidence: 99%

“…Earlier, topological indices from graph theory [10] were widely used because they can easily be calculated if the molecular structure is known, there exists more than 120 different topological indices [11]. One of the most popular indices in quantitative structure properties relation applications is the connectivity index [12] which measures the degree of branching.…”

Section: Introductionmentioning

confidence: 99%

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The use of an optimized RP-HPLC system as a molecular probe in QSPR studies of selected lipid classes

Robertsson

Andersson

Kaufmann³

1998

Chromatographia

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Key WordsColumn liquid chromatography Quantitative structure retention relationships Quantitative structure properties relationships Phospholipids Molecular probe SummaryThe results of this study show that an optimized RP-HPLC system, in conjunction with molecular mechanics, can be used as a molecular probe to study both configuration and conformation of molecular species of selected phospholipid classes. Specifically, for phosphatidylcholine 18:0/16:0, stearic acid is attached to the sn-1 position and palmitic acid is attached to the sn-2 position of the glycerol backbone, for phosphatidylcholine with two monounsaturated fatty acids, the monounsaturated fatty acid attached to the sn-1 position can fold itself backwards on itself, thus allowing van der Waals interaction. Furthermore, it was found in the retention modelling that configurational descriptors alone did not suffice but had to be augmented with conformational descriptors. Nonlinearities were also detected, which could be handled by using a hybrid neural network-PLS regression strategy.

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Section: Molecular Descriptorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The use of an optimized RP-HPLC system as a molecular probe in QSPR studies of selected lipid classes

Robertsson

Andersson

Kaufmann³

1998

Chromatographia

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“…(11). It may be that the formulas (14) and (15) are reported here for the first time. The above three expressions suggest that also for k > 3, the following invariants may be of some relevance in mathematical chemistry:…”

Section: Hosoya Polynomialmentioning

confidence: 72%

On a class of distance-based molecular structure descriptors

Bruckler¹,

Došlić²,

Graovac³

et al. 2011

Chemical Physics Letters

100

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“…(1) (G), and the so-called Tratch-Stankevich-Zefirov index T SZ(G) of G [24] was shown [18] to be equal to …”

mentioning

confidence: 99%

“…Recall that, the hyper-Wiener and the Tratch-Stankevich-Zefirov indices were originally defined in terms completely different from the presently considered Wiener-type invariants; for details see [22,24].…”

mentioning

confidence: 99%

Clusters and various versions of wiener-type invariants

Azari¹,

Iranmanesh²

2015

Kragujevac J Math

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Abstract. The Wiener type invariant W (λ) (G) of a simple connected graph G is defined as the sum of the terms d (u, v |G ) λ over all unordered pairs {u, v} of vertices of G, where d(u, v|G) denotes the distance between the vertices u and v in G and λ is an arbitrary real number. The cluster G 1 {G 2 } of a graph G 1 and a rooted graph G 2 is the graph obtained by taking one copy of G 1 and |V (G 1 )| copies of G 2 , and by identifying the root vertex of the i-th copy of G 2 with the i-th vertex of G 1 , for i = 1, 2, . . . , |V (G 1 )|. In this paper, we study the behavior of three versions of Wiener type invariant under the cluster product. Results are applied to compute several distance-based topological invariants of bristled and bridge graphs by specializing components in clusters.

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Combinatorial models and algorithms in chemistry. The expanded Wiener number—a novel topological index

Abstract: An expanded form of the Wiener number is suggested for characterization of molecular graphs and structure‐property correlations. The simple, computer‐oriented method for counting of the novel index is briefly discussed.

Cited by 75 publications

References 23 publications

The use of an optimized RP-HPLC system as a molecular probe in QSPR studies of selected lipid classes

The use of an optimized RP-HPLC system as a molecular probe in QSPR studies of selected lipid classes

On a class of distance-based molecular structure descriptors

Clusters and various versions of wiener-type invariants

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