scholarly journals Predicting Some Physicochemical Properties of Octane Isomers: A Topological Approach Using ev-Degree and ve-Degree Zagreb Indices

2017 ◽  
Author(s):  
Süleyman Ediz
Keyword(s):  
Physicochemical Properties ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Graph Invariants ◽  
Zagreb Index ◽  
Topological Approach ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Octane Isomers ◽  
Mathematical Literature

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study we define ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index by using these new graph invariants as parallel to their corresponding classical degree versions. We compare these new group ev-degree and ve-degree indices with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. We investigate the relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices.

scholarly journals HDR Degree Bassed Indices and Mhr-Polynomial for the Treatment of COVID-19

2021 ◽  
Vol 12 (6) ◽  
pp. 7214-7225
Keyword(s):  
Regression Analysis ◽  
Physicochemical Properties ◽  
Topological Index ◽  
Research Work ◽  
Topological Indices ◽  
Structure Property ◽  
Zagreb Index ◽  
Mathematical Properties ◽  
Octane Isomers

In this research work, We introduce topological indices, namely as an HDR version of Modified Zagreb topological index (HDRM*), HDR version of Modified forgotten topological index (HDRF*), and HDR version of hyper Zagreb index (HDRHM*). Then the relatively study depends on the structure-property regression analysis to test and compute the chemical applicability of these indices to predict the physicochemical properties of octane isomers. Also, we show these HDR indices have well degeneracy properties compared to other degree-based topological indices. Also, We defined and computed the Mhr-polynomial of the newly indices and applied it on COVID-19 treatments. Also, we discussed some mathematical properties of HDR indices.

scholarly journals Onsome New Neighbourhood Degree Based Indices

2019 ◽  
Vol 27 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Regression Analysis ◽  
Physicochemical Properties ◽  
Topological Index ◽  
Topological Indices ◽  
Structure Property ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Mathematical Properties ◽  
Octane Isomers

Abstract In this paper, four novel topological indices named as neighbourhood version of forgotten topological index (FN), modified neighbourhood version of Forgotten topological index (FN*), neighbourhood version of second Zagreb index (M2*) and neighbourhood version of hyper Zagreb index (HMN) are introduced. Here the relatively study depends on the structure-property regression analysis is made to test and compute the chemical applicability of these indices for the prediction of physicochemical properties of octane isomers. Also it is shown that these newly presented indices have well degeneracy property in comparison with other degree based topological indices. Some mathematical properties of these indices are also discussed here.

scholarly journals Zagreb Connection Indices of Two Dendrimer Nanostars

2019 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Nisar Fatima ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Physicochemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Mathematical Chemistry ◽  
Octane Isomers ◽  
The First Zagreb Index

Abstract It is well known fact that several physicochemical properties of chemical compounds are closely related to their molecular structure. Mathematical chemistry provides a method to predict the aforementioned properties of compounds using topological indices. The Zagreb indices are among the most studied topological indices. Recently, three modified versions of the Zagreb indices were proposed independently in [Ali, A.; Trinajstić, N. A novel/old modification of the first Zagreb index, arXiv:1705.10430 [math.CO] 2017; Mol. Inform. 2018, 37, 1800008] and [Naji, A. M.; Soner, N. D.; Gutman, I. On leap Zagreb indices of graphs, Commun. Comb. Optim. 2017, 2, 99–117], which were named as the Zagreb connection indices and the leap Zagreb indices, respectively. In this paper, we check the chemical applicability of the newly considered Zagreb connection indices on the set of octane isomers and establish general expressions for calculating these indices of two well-known dendrimer nanostars.

A Novel Weighted First Zagreb Index of Graph

2020 ◽  
pp. 92-103
Author(s):  
Jibonjyoti Buragohain ◽  
A. Bharali
Keyword(s):  
Connected Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Acentric Factor ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Physico Chemical ◽  
Octane Isomers ◽  
The First Zagreb Index

The Zagreb indices are the oldest among all degree-based topological indices. For a connected graph G, the first Zagreb index M1(G) is the sum of the term dG(u)+dG(v) corresponding to each edge uv in G, that is, M1 , where dG(u) is degree of the vertex u in G. In this chapter, the authors propose a weighted first Zagreb index and calculate its values for some standard graphs. Also, the authors study its correlations with various physico-chemical properties of octane isomers. It is found that this novel index has strong correlation with acentric factor and entropy of octane isomers as compared to other existing topological indices.

Degree-based topological indices of double graphs and strong double graphs

2017 ◽  
Vol 09 (05) ◽  
pp. 1750066 ◽  
Author(s):  
Muhammad Imran ◽  
Shehnaz Akhter
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Boiling Point ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Original Graph ◽  
Zagreb Index ◽  
Zagreb Indices

The topological indices are useful tools to the theoretical chemists that are provided by the graph theory. They correlate certain physicochemical properties such as boiling point, strain energy, stability, etc. of chemical compounds. For a graph [Formula: see text], the double graph [Formula: see text] is a graph obtained by taking two copies of graph [Formula: see text] and joining each vertex in one copy with the neighbors of corresponding vertex in another copy and strong double graph SD[Formula: see text] of the graph [Formula: see text] is the graph obtained by taking two copies of the graph [Formula: see text] and joining each vertex [Formula: see text] in one copy with the closed neighborhood of the corresponding vertex in another copy. In this paper, we compute the general sum-connectivity index, general Randi[Formula: see text] index, geometric–arithmetic index, general first Zagreb index, first and second multiplicative Zagreb indices for double graphs and strong double graphs and derive the exact expressions for these degree-base topological indices for double graphs and strong double graphs in terms of corresponding index of original graph [Formula: see text].

Tetracyclic graphs with maximum second Zagreb index: A simple approach

2018 ◽  
Vol 11 (05) ◽  
pp. 1850064 ◽  
Author(s):  
Akbar Ali
Keyword(s):  
Graph Theory ◽  
Short Note ◽  
Topological Indices ◽  
Simple Approach ◽  
Graph Invariants ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Chemical Graph Theory

In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum [Formula: see text] value among all members of the collection [Formula: see text]. In this short note, an alternative but relatively simple approach is used for characterizing the aforementioned graph.

scholarly journals Mathematical Properties of Variable Topological Indices

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 43
Author(s):  
José M. Sigarreta
Keyword(s):  
Real Number ◽  
Large Class ◽  
Symmetric Functions ◽  
Topological Indices ◽  
Current Interest ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Connectivity Indices ◽  
Optimal Bounds ◽  
New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

scholarly journals Computation of Zagreb and atom-bond connectivity indices of certain families of dendrimers by using automorphism group action

2017 ◽  
Vol 82 (2) ◽  
pp. 151-162
Author(s):  
Uzma Ahmad ◽  
Sarfraz Ahmad ◽  
Rabia Yousaf
Keyword(s):  
Automorphism Group ◽  
Carbon Atom ◽  
Physicochemical Properties ◽  
Group Action ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Connectivity Indices ◽  
Atom Bond

In QSAR/QSPR studies, topological indices are utilized to predict the bioactivity of chemical compounds. In this paper, the closed forms of different Zagreb indices and atom?bond connectivity indices of regular dendrimers G[n] and H[n] in terms of a given parameter n are determined by using the automorphism group action. It was reported that these connectivity indices are correlated with some physicochemical properties and are used to measure the level of branching of the molecular carbon-atom skeleton.

On degree-based topological descriptors of strong product graphs

2016 ◽  
Vol 94 (6) ◽  
pp. 559-565 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Zagreb Indices ◽  
Strong Product ◽  
Product Graphs ◽  
Product Of Graphs ◽  
Atom Bond

Topological descriptors are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity, and geometric–arithmetic are used to predict the bioactivity of different chemical compounds. There are certain types of topological descriptors such as degree-based topological indices, distance-based topological indices, counting-related topological indices, etc. Among degree-based topological indices, the so-called atom–bond connectivity and geometric–arithmetic are of vital importance. These topological indices correlate certain physicochemical properties such as boiling point, stability, strain energy, etc., of chemical compounds. In this paper, analytical closed formulas for Zagreb indices, multiplicative Zagreb indices, harmonic index, and sum-connectivity index of the strong product of graphs are determined.

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