Alkanes with the First Three Maximal/Minimal Modified First Zagreb Connection Indices

Du, Zhibin; Ali, Akbar; Trinajstić, Nenad

doi:10.1002/minf.201800116

Cited by 36 publications

(23 citation statements)

References 20 publications

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“…Corresponding to these degree-based TIs, the connection-based TIs are defined in Definition 2. For further studies of connection-based TIs, see [21,22,44].…”

Section: Preliminariesmentioning

confidence: 99%

“…ey also reported that it has more precise values of the correlation coefficients of various octane isomers. Du et al [22], Ducoffe et al [23], and Shao et al [24] determined extremal alkanes and cycloalkanes under different conditions using this ZCI. Zhu et al [25] established the lower bound by using the modified first ZCI of trees in terms of their order and maximum degree.…”

Section: Introductionmentioning

confidence: 99%

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Zagreb Connection Indices of Molecular Graphs Based on Operations

et al. 2020

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Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. The Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic Mol. Inform. 372018,1−7 restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included.

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“…Corresponding to these degree-based TIs, the connection-based TIs are defined in Definition 2. For further studies of connection-based TIs, see [21,22,44].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Zagreb Connection Indices of Molecular Graphs Based on Operations

et al. 2020

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“…It was appeared after a long gap, due to that instance, (M 3 (G)) -index is also known as forgotten index (F(G)). At present time, so many TI's have been explored with their properties and they have revolutionized the fruitful results in the study of science especially in the lattest field of cheminformatics that is the combination of three subjects Mathematics, Chemistry and Information Technology (Borovicanin et al, 2017;Das and Gutman, 2004;Liu et al, 2019aShirinivas et al, 2010;Todeschini and Consonni, 2002), Therefore, degree based TI's are more studied and well applicabled (Du et al, 2019;Liu et al, 2019bLiu et al, , 2020Tang et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Modified Zagreb connection indices of the T-sum graphs

Ali

Javaid

Kashif

2020

Main Group Metal Chemistry

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The quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI’s such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

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“…ey also reported (as per data provided by the International Academy of Mathematical Chemistry) that its chemical capability has more precise correlation coefficient values for the following thirteen physicochemical properties of octane isomers: density, heat capacity at temperature, standard enthalpy of vaporization, boiling point, heat capacity at pressure, enthalpy of vaporization, entropy, acentric factor, molar volume, total surface area, enthalpy of formation, standard enthalpy of formation, and octanol water partition coefficient. Du et al [31] determined extremal alkanes by using modified first Zagreb connection index. In the same year, Ducoffe et al [32] also characterized extremal graphs with respect to the modified first Zagreb connection index for trees and unicyclic graphs with or without a fixed girth.…”

Section: Introductionmentioning

confidence: 99%

Zagreb Connection Indices of Subdivision and Semi-Total Point Operations on Graphs

Tang

Ali

Javaid

et al. 2019

Journal of Chemistry

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Representation or coding of the molecular graphs with the help of numerical numbers plays a vital role in the studies of physicochemical and structural properties of the chemical compounds that are involved in the molecular graphs. For the first time, the modified first Zagreb connection index appeared in the paper by Gutman and Trinajstic (1972) to compute total electron energy of the alternant hydrocarbons, but after that, for a long time, it has not been studied. Recently, Ali and Trinajstic (2018) restudied the first Zagreb connection index ZC1, the second Zagreb connection index ZC2, and the modified first Zagreb connection index ZC1∗ to find entropy and acentric factor of the octane isomers. They also reported that the values provided by the International Academy of Mathematical Chemistry show better chemical capability of the Zagreb connection indices than the ordinary Zagreb indices. Assume that S1 and S2 denote the operations of subdivision and semitotal point, respectively. Then, the S-sum graphs Q1+QS2 are obtained by the cartesian product of SQ1 and Q2, where S∈S1,S2, Q1andQ2 are any connected graphs, and SQ1 is a graph obtained after applying the operation S on Q1. In this paper, we compute the Zagreb connection indices (ZC1, ZC2, and ZC1∗) of the S-sum graphs in terms of various topological indices of their factor graphs. At the end, as an application of the computed results, the Zagreb connection indices of the S-sum graphs obtained by the particular classes of alkanes are also included.

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Alkanes with the First Three Maximal/Minimal Modified First Zagreb Connection Indices

Cited by 36 publications

References 20 publications

Zagreb Connection Indices of Molecular Graphs Based on Operations

Zagreb Connection Indices of Molecular Graphs Based on Operations

Modified Zagreb connection indices of the T-sum graphs

Zagreb Connection Indices of Subdivision and Semi-Total Point Operations on Graphs

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