Extremal Graphs with Respect to the Modified First Zagreb Connection Index

Ducoffe, Guillaume; Marinescu-Ghemeci, Ruxandra; Obreja, Camelia; Popa, Alexandru; Tache, Rozica Maria

doi:10.1109/synasc.2018.00033

Cited by 24 publications

(19 citation statements)

References 4 publications

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“…Some recent extremal results on the topological index ZC Ã 1 can be found in. [25,26] The purpose of the present study is to extend the main results of the paper, [10] or more precisely, to find the alkanes with the first three maximal and the first three minimal ZC Ã 1 values from the class of all n-vertex molecular trees.…”

Section: Introductionmentioning

confidence: 90%

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

Ali

Trinajstić

2019

Molecular Informatics

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The modified first Zagreb connection index (ZC Ã 1 ) is a molecular descriptor, which was initially appeared within a formula of the total electron energy of alternant hydrocarbons in 1972. In a recent paper [A. Ali, N. Trinajstić, A novel/old modification of the first Zagreb index, Mol. Inform. 37 (2018) 1800008], it was observed that the molecular descriptor ZC Ã 1 correlates well with the entropy and acentric factor of octane isomers. In this article, the molecules with the first three maximal ZC Ã 1 values as well as the first three minimal ZC Ã 1 values are determined from the family of all alkanes with n carbon atoms, for n ! 6. This extends the main results of the aforementioned paper.

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Section: Introductionmentioning

confidence: 90%

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

Ali

Trinajstić

2019

Molecular Informatics

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“…Thus, Problem 1.1 is well-defined for 3 ≤ k ≤ n − 1. Also, Ducoffe et al [30] proved that the star graph S n has the maximal ZC * 1 value among all the nvertex trees, which implies that S n has the maximal ZC * 1 value among all the members of T n,n−1 as well. Consequently, while solving Problem 1.1 concerning maximal ZC * 1 value, we will consider the constrain 3 ≤ k ≤ n − 2, and while solving the remaining part of Problem 1.1 we will assume 3 ≤ k ≤ n − 1.…”

Section: Problem 11: Characterize All the Graphs With The Maximal/mimentioning

confidence: 99%

“…It needs to be mentioned here that the index ZC * 1 was referred as the third leap Zagreb index in [26]. After appearance of the papers [14,26], mathematical properties of the modified first Zagreb connection index ZC * 1 have been studied in a considerable number of papers [26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Extremal trees for the modified first Zagreb connection index with fixed number of segments or vertices of degree 2

Noureen

Bhatti

Ali

2019

Journal of Taibah University for Science

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“…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%

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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Extremal Graphs with Respect to the Modified First Zagreb Connection Index

Cited by 24 publications

References 4 publications

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

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

Extremal trees for the modified first Zagreb connection index with fixed number of segments or vertices of degree 2

Zagreb Connection Indices of Molecular Graphs Based on Operations

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