Eccentricity based topological indices of honeycomb networks

Imran, Muhammad; Abunamous, Amna A. E.; Adi, Dana; Rafique, Sadia Hafa; Baig, Abdul Qudair; Farahani, Mohammad Reza

doi:10.1080/09720529.2019.1691326

Cited by 22 publications

(3 citation statements)

References 13 publications

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“… Total Eccentricity index The total eccentricity is defined as the addition of eccentricity of all the vertices.

For further details about this index see [44] , [45] , [46] , [47] First Zagreb eccentric index Gutman and Trinajstic introduced the Zagreb type indices [48] . Later, Ghorbani proposed the modified version of first Zagreb index in terms of eccentricity [49] as given below:

Augmented eccentric-connectivity index Gupta et al [50] suggested the augmented eccentric-connectivity index of a graph

and it is specified as:

where

is the product of degrees of all the neighboring vertices of a .…”

Section: Distance-based Topological Descriptorsmentioning

confidence: 99%

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On eccentricity-based entropy measures for dendrimers

Huang

Siddiqui

Manzoor

et al. 2021

Heliyon

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The eccentricity-based entropy inspired by Shannon's entropy approach is the information-theoretic quantity to figure out the structural information of complex networks. The investigation for advance biomedical utilization of dendrimers has improved the synthesis of radical based molecules. Categorically, attaining radical dendrimers has initiated their use in different fields such as anti-tumor agents and as magnetic resonance imaging. The use of radical dendrimers has increased the possibility of establishing new kinds of devices based on para-magnetic axioms of organic radicals. In this article, we discussed dendrimer based on cyclotriphosphazene ( ) which has balanced edge groups and these are examined by EPR temperature spectrum. Firstly, we computed eccentricity-based indices and then we computed eccentricity based entropies by developing an acquaintance between these indices and their entropies. Moreover we presented our computed result numerically and graphically which leads to good importance of our contribution.

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“… Total Eccentricity index The total eccentricity is defined as the addition of eccentricity of all the vertices.

Augmented eccentric-connectivity index Gupta et al [50] suggested the augmented eccentric-connectivity index of a graph

and it is specified as:

where

is the product of degrees of all the neighboring vertices of a .…”

Section: Distance-based Topological Descriptorsmentioning

confidence: 99%

“…For further details about this index see [25,26,24,32] • First Zagreb eccentric index Gutman and Trinajstic introduced the Zagreb type indices [31] . Later, Ghorbani proposed the modified version of first Zagreb index in terms of eccentricity [28] as given bellow:…”

Section: • Total Eccentricity Indexmentioning

confidence: 99%

On eccentricity-based entropy measures for dendrimers

Huang

Siddiqui

Manzoor

et al. 2021

Heliyon

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“…Zagreb eccentricity indices have been investigated due to their wide applications. Eccentricity based indices of honeycomb networks were studied in [6], nanostar dendrimers in [3] and oxid networks in [8], For related works, see [1], [2], [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Extended study of biological networks using graph theory

Vetrík

2021

Proyecciones (Antofagasta)

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We represent biological networks by a function that maps the structure of a network to a number called topological index. Topological indices have been studied for biological networks in which a person transmits a virus to two other people, and a person having the virus is in contact with exactly one other person who got the virus from someone else. We extend research in this area by studying biological networks in which a person transmits a virus to n other people, where n ≥ 2, and a person having the virus is in contact with p other people (0 ≤ p ≤ n-2) who got the virus from some other person.

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