Eccentric Connectivity Index of <i>t</i>-Polyacenic Nanotubes

Liu, Jia‐Bao; Shaker, Hani; Nadeem, Imran; Farahani, Mohammad Reza

doi:10.1155/2019/9062535

Cited by 4 publications

(2 citation statements)

References 29 publications

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“…In [15], Sharma et al introduced the eccentric connectivity index of the graph M as ξ c (M) � 􏽐 v∈V(M) d(v)e(v). For mathematical properties, the interested readers can consult [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Leap Eccentric Connectivity Index of Subdivision Graphs

Ghalavand

Pawar

Soner

2022

Journal of Mathematics

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The second degree of a vertex in a simple graph is defined as the number of its second neighbors. The leap eccentric connectivity index of a graph M , L ξ c M , is the sum of the product of the second degree and the eccentricity of every vertex in M . In this paper, some lower and upper bounds of L ξ c S M in terms of the numbers of vertices and edges, diameter, and the first Zagreb and third leap Zagreb indices are obtained. Also, the exact values of L ξ c S M for some well-known graphs are computed.

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Section: Introductionmentioning

confidence: 99%

Leap Eccentric Connectivity Index of Subdivision Graphs

Ghalavand

Pawar

Soner

2022

Journal of Mathematics

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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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Topological and Thermodynamic Entropy Measures for COVID-19 Pandemic through Graph Theory

et al. 2020

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Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an integral part of artificial intelligence are designed for contact tracing, genetic network analysis for uncovering the biological evolution of the virus, understanding the underlying mechanisms of the observed disease dynamics, evaluating mitigation strategies, and predicting the COVID-19 pandemic dynamics. This paper describes mathematical techniques to exploit and understand the progression of the pandemic through a topological characterization of underlying graphs. We have obtained several topological indices for various graphs of biological interest such as pandemic trees, Cayley trees, Christmas trees, and the corona product of Christmas trees and paths. We have also obtained an analytical expression for the thermodynamic entropies of pandemic trees as a function of R0, the reproduction number, and the level of spread, using the nested wreath product groups. Our plots of entropy and logarithms of topological indices of pandemic trees accentuate the underlying severity of COVID-19 over the 1918 Spanish flu pandemic.

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Eccentric Connectivity Index of t-Polyacenic Nanotubes

Cited by 4 publications

References 29 publications

Leap Eccentric Connectivity Index of Subdivision Graphs

Leap Eccentric Connectivity Index of Subdivision Graphs

Extended study of biological networks using graph theory

Topological and Thermodynamic Entropy Measures for COVID-19 Pandemic through Graph Theory

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