On the Number of Matchings of Two Classes of Silicate Molecular Graphs

Background: Recently, some authors have defined new molecular descriptors (MDs) based on the use of the Graph Discrete Derivative, known as Graph Derivative Indices (GDI). This new approach about discrete derivatives over various elements from a graph takes as outset the formation of subgraphs. Previously, these definitions were extended into the chemical context (N-tuples) and interpreted in structural/physicalchemical terms as well as applied into the description of several endpoints, with good results. Objective: A generalization of GDIs using the definitions of Higher Order and Mixed Derivative for molecular graphs is proposed as a generalization of the previous works, allowing the generation of a new family of MDs. Methods: An extension of the previously defined GDIs is presented, and for this purpose, the concept of Higher Order Derivatives and Mixed Derivatives is introduced. These novel approaches to obtaining MDs based on the concepts of discrete derivatives (finite difference) of the molecular graphs use the elements of the hypermatrices conceived from 12 different ways (12 events) of fragmenting the molecular structures. The result of applying the higher order and mixed GDIs over any molecular structure allows finding Local Vertex Invariants (LOVIs) for atom-pairs, for atoms-pairs-pairs and so on. All new families of GDIs are implemented in a computational software denominated DIVATI (acronym for Discrete DeriVAtive Type Indices), a module of KeysFinder Framework in TOMOCOMD-CARDD system. Results: QSAR modeling of the biological activity (Log 1/K) of 31 steroids reveals that the GDIs obtained using the higher order and mixed GDIs approaches yield slightly higher performance compared to previously reported approaches based on the duplex, triplex and quadruplex matrix. In fact, the statistical parameters for models obtained with the higher-order and mixed GDI method are superior to those reported in the literature by using other 0-3D QSAR methods. Conclusion: It can be suggested that the higher-order and mixed GDIs, appear as a promissory tool in QSAR/QSPRs, similarity/dissimilarity analysis and virtual screening studies.

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Constraints for generating graphs with imposed and forbidden patterns: an application to molecular graphs

Constraints ◽

10.1007/s10601-019-09305-x ◽

2019 ◽

Vol 25 (1-2) ◽

pp. 1-22

Author(s):

Mohamed Amine Omrani ◽

Wady Naanaa

Keyword(s):

Molecular Graphs ◽

Forbidden Patterns

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Topological Indices of Para-line Graphs of V-Phenylenic Nanostructures

Open Mathematics ◽

10.1515/math-2019-0020 ◽

2019 ◽

Vol 17 (1) ◽

pp. 260-266 ◽

Cited By ~ 2

Author(s):

Imran Nadeem ◽

Hani Shaker ◽

Muhammad Hussain ◽

Asim Naseem

Keyword(s):

Chemical Properties ◽

Topological Indices ◽

Structural Chemistry ◽

Line Graphs ◽

Physical And Chemical Properties ◽

Graph Invariants ◽

Molecular Graphs ◽

Physical And Chemical ◽

And Chemical Properties

Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

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The Pt site reactivity of the molecular graphs of Au6Pt isomers

Chemical Physics Letters ◽

10.1016/j.cplett.2013.10.059 ◽

2013 ◽

Vol 590 ◽

pp. 41-45 ◽

Cited By ~ 10

Author(s):

Tianlv Xu ◽

Samantha Jenkins ◽

Chen-Xia Xiao ◽

Julio R. Maza ◽

Steven R. Kirk

Keyword(s):

Molecular Graphs

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Methods and algorithms for predicting the properties of chemical compounds by common fragments of molecular graphs

Journal of Structural Chemistry ◽

10.1007/bf02873831 ◽

1998 ◽

Vol 39 (1) ◽

pp. 93-102 ◽

Cited By ~ 1

Author(s):

L. I. Makarov

Keyword(s):

Chemical Compounds ◽

Molecular Graphs

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ON MOSTAR INDEX OF GRAPHS

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.4.26 ◽

2021 ◽

Vol 10 (4) ◽

pp. 2115-2129

Author(s):

P. Kandan ◽

S. Subramanian

Keyword(s):

Connected Graph ◽

Cartesian Product ◽

Bipartite Graphs ◽

Topological Indices ◽

Great Success ◽

Complete Graphs ◽

Molecular Graphs ◽

Graphs And Networks ◽

Complete Bipartite Graphs ◽

Simple Connected Graph

On the great success of bond-additive topological indices like Szeged, Padmakar-Ivan, Zagreb, and irregularity measures, yet another index, the Mostar index, has been introduced recently as a peripherality measure in molecular graphs and networks. For a connected graph G, the Mostar index is defined as $$M_{o}(G)=\displaystyle{\sum\limits_{e=gh\epsilon E(G)}}C(gh),$$ where $C(gh) \,=\,\left|n_{g}(e)-n_{h}(e)\right|$ be the contribution of edge $uv$ and $n_{g}(e)$ denotes the number of vertices of $G$ lying closer to vertex $g$ than to vertex $h$ ($n_{h}(e)$ define similarly). In this paper, we prove a general form of the results obtained by $Do\check{s}li\acute{c}$ et al.\cite{18} for compute the Mostar index to the Cartesian product of two simple connected graph. Using this result, we have derived the Cartesian product of paths, cycles, complete bipartite graphs, complete graphs and to some molecular graphs.

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