On the Randić index

Delorme, Charles; Favaron, Odile; Rautenbach, Dieter

doi:10.1016/s0012-365x(02)00256-x

Cited by 59 publications

(41 citation statements)

References 11 publications

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“…Bollobos i P. Erdos re{avaju problem kada je k = 1 [4]; odgovaraju}i graf je zvezda S n . Za k = 2 re{ewe je dato u [10] i odgovaraju}i graf je K * 2,n−2 . Oba ova slu~aja su re{ena analizom same strukture grafa, tzv.…”

Section: 2unclassified

“…Tako|e, izostavqawe jedne grane uv dovodi do promene vrednosti Randi}evog indeksa grafa G promenom te`ina ostalih grana. Ovde navodimo tvr|ewe koja se koristi u dokazima za nala`ewe minimuma Randi}evog indeksa na grafovima minimalnog stepena~vorova k = 1 [4], kasnije i k = 2 [10].…”

Section: Matemati~ke Metodeunclassified

“…Re{avaju}i problem za k = 2, C. Delorme, O. Favaron i D. Rautenbach [10] postavqaju i prvu pretpostavku op{teg re{ewa. [33].…”

Section: Hipoteze I Opis Problemaunclassified

“…U ovoj glavi je, pored izno{ewa ovih metoda, dat i prikaz nekih rezultata. Do prvih rezultata, odre|ivawe maksimalne vrednosti Randi}evog indeksa na prostim grafovima [14] , odre|ivawe minimuma Randi}evog indeksa za grafove minimalnog stepena~vorova jedan, dva, pa onda i tri dolazi se, prvo, grafovskom tehnikom [4,10], a zatim i linearnim programirawem [28,30,25]. Upravo jedan od tih po~etnih rezultata, odre|ivawe minimuma Randi}evog indeksa na prostim grafovima bez izolovanih~vorova je, uz izvesne promene, i predstavqen u ovoj glavi.…”

unclassified

“…Dobijenim rezultatom je kona~no dokazana hipoteza koja je postavqena prvi put u radu [10], a zatim preciznije u [1] i na kraju u [27]. Do tog rezultata je bilo o~igledno te{ko do}i s obzirom da je posledwi dokazan.…”

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Neki rezultati o ekstremnim vrednostima Randicevog indeksa na grafovima

Divnić¹

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Section: 2unclassified

Section: Matemati~ke Metodeunclassified

“…Re{avaju}i problem za k = 2, C. Delorme, O. Favaron i D. Rautenbach [10] postavqaju i prvu pretpostavku op{teg re{ewa. [33].…”

Section: Hipoteze I Opis Problemaunclassified

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Neki rezultati o ekstremnim vrednostima Randicevog indeksa na grafovima

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Quantitative structure–property relationship of Ev‐degree and Ve‐degree based topological indices : physico‐chemical properties of benzene derivatives

Rauf

Bukhari²

2021

Int J of Quantum Chemistry

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A quantitative structure-property relationship study was performed for the prediction of physical properties of 22 benzene derivatives using ev-degree and ve-degree topological indices. These topological indices correlate certain physico-chemical property with the chemical structure (like molecular weight, enthalpy, boiling point and π-electron energy of β-unit of benzene derivatives). At first, a simple linear regression model was developed using ve-degree and ev-degree topological indices and the certain physical properties of the considered benzene derivatives. It is found that the atom bond connectivity index (ABC ve ) possesses the best correlating ability among several topological indices to predict the boiling point, the ve-degree based Randi c index R ve is the best predictor of enthalpy, the ev degree based Randi c index R ev is the best predictor of π-electron energy, the sum connectivity index χve is the best predictor of molecular weight. Second, multiple linear regressions were used for prediction the physical properties (molecular weight, boiling point, enthalpy and π-electron energy of β-unit) on the basis of six predictor such as M βve 1 , M βve 2 , GA ve , χ ve , R ve , and H ve indices. This multi-linear regression model shows the 100% variation in π-electron energy of β-unit. A Maple software based algorithm is used for the calculations of topological indices and the statistical analysis is performed with the SPSS software. The calculations of the ev and ve degree based topological indices of chemical structure of styrene-butadiene rubber are presented at the end to illustrate the given Maple algorithm.

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Topological indices and entropy of twisted cylinder‐nonorientable hexagonal Mobius strip

Qasim

Shaker

Zobair

2023

Int J of Quantum Chemistry

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Mobius strip is an infinite loop having one‐sided surface with no boundaries, also known as twisted cylinder. Möbius strips being widely used in different fields of engineering are of important nature in research. Being different in sizes and shapes, these can be visualized in Euclidean space but few cannot be. Topology of Mobius strips makes it a rare Euclidean representation of the infinite nature. Researchers expanded this concept and generalized it in the form of Klein bottles. In this article, we have derived various polynomials and respective topological indices for the Hexagonal Möbius graphs having each face as a hexagon. Also, inverse relationship between heat of formation and crystal size is developed for the calculated indices.

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On the Randić index

Cited by 59 publications

References 11 publications

Neki rezultati o ekstremnim vrednostima Randicevog indeksa na grafovima

Neki rezultati o ekstremnim vrednostima Randicevog indeksa na grafovima

Quantitative structure–property relationship of Ev‐degree and Ve‐degree based topological indices : physico‐chemical properties of benzene derivatives

Topological indices and entropy of twisted cylinder‐nonorientable hexagonal Mobius strip

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