Second order Randić index of phenylenes and their corresponding hexagonal squeezes

The connectivity index of an organic molecule whose molecular graph is Gis defined as C(?)=?(?u?v)??where ?u is the degree of the vertex u in G, where the summation goes over all pairs of adjacent vertices of G and where ? is a pertinently chosen exponent. The usual value of ? is ?1/2, in which case ?=C(?1/2) is referred to as the Randic index. The ordering of isomeric alkanes according to ??follows the extent of branching of the carbon-atom skeleton. We now study the ordering of the constitutional isomers of alkanes with 6 through 10 carbon atoms with respect to C(?) for various values of the parameter ?. This ordering significantly depends on ?. The difference between the orderings with respect to ??and with respect to C(?) is measured by a function ??and the ?-dependence of ??was established.

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The exponent in the general Randić index

Journal of Mathematical Chemistry ◽

10.1007/s10910-006-9177-7 ◽

2006 ◽

Vol 43 (1) ◽

pp. 32-44 ◽

Cited By ~ 9

Author(s):

Lane Clark ◽

Ivan Gutman

Keyword(s):

Randić Index ◽

Randic Index ◽

General Randić Index ◽

General Randic Index

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On the conjecture of Aouchiche and Hansen about the Randić index

Discrete Mathematics ◽

10.1016/j.disc.2012.10.012 ◽

2013 ◽

Vol 313 (3) ◽

pp. 225-235 ◽

Cited By ~ 6

Author(s):

Bolian Liu ◽

Ljiljana R. Pavlović ◽

Tomica R. Divnić ◽

Jianxi Liu ◽

Marina M. Stojanović

Keyword(s):

Randić Index ◽

Randic Index

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Bounds on General Randić Index for F-Sum Graphs

Journal of Mathematics ◽

10.1155/2020/9129365 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Xu Li ◽

Maqsood Ahmad ◽

Muhammad Javaid ◽

Muhammad Saeed ◽

Jia-Bao Liu

Keyword(s):

Molecular Graph ◽

Randić Index ◽

Lower And Upper Bounds ◽

First Zagreb Index ◽

Zagreb Index ◽

Randic Index ◽

Structure Activity ◽

General Randić Index ◽

General Randic Index ◽

The First Zagreb Index

A topological invariant is a numerical parameter associated with molecular graph and plays an imperative role in the study and analysis of quantitative structure activity/property relationships (QSAR/QSPR). The correlation between the entire π-electron energy and the structure of a molecular graph was explored and understood by the first Zagreb index. Recently, Liu et al. (2019) calculated the first general Zagreb index of the F-sum graphs. In the same paper, they also proposed the open problem to compute the general Randić index RαΓ=∑uv∈EΓdΓu×dΓvα of the F-sum graphs, where α∈R and dΓu denote the valency of the vertex u in the molecular graph Γ. Aim of this paper is to compute the lower and upper bounds of the general Randić index for the F-sum graphs when α∈N. We present numerous examples to support and check the reliability as well as validity of our bounds. Furthermore, the results acquired are the generalization of the results offered by Deng et al. (2016), who studied the general Randić index for exactly α=1.

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First General Zagreb Index of Generalized F-sum Graphs

Discrete Dynamics in Nature and Society ◽

10.1155/2020/2954975 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

H. M. Awais ◽

Muhammad Javaid ◽

Akbar Ali

Keyword(s):

Real Number ◽

Cartesian Product ◽

Randić Index ◽

Zeroth Order ◽

Zagreb Index ◽

Randic Index

The first general Zagreb (FGZ) index (also known as the general zeroth-order Randić index) of a graph G can be defined as M γ G = ∑ u v ∈ E G d G γ − 1 u + d G γ − 1 v , where γ is a real number. As M γ G is equal to the order and size of G when γ = 0 and γ = 1 , respectively, γ is usually assumed to be different from 0 to 1. In this paper, for every integer γ ≥ 2 , the FGZ index M γ is computed for the generalized F-sums graphs which are obtained by applying the different operations of subdivision and Cartesian product. The obtained results can be considered as the generalizations of the results appeared in (IEEE Access; 7 (2019) 47494–47502) and (IEEE Access 7 (2019) 105479–105488).

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