Topological properties of Graphene using some novel neighborhood degree-based topological indices

Mondal, Sourav; De, Nilanjan; Pal, Anita

doi:10.1142/s2661335219500060

Cited by 37 publications

(13 citation statements)

References 14 publications

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“…is the degree sum of neighbour vertices of 𝑣 in 𝑉(𝐺). This descriptor is defined by [17] and studied by [18][19][20][21][22][23].…”

Section: 𝑢𝑣∈𝐸(𝐺)mentioning

confidence: 99%

Generalized Second Neighborhood Zagreb Index: Mathematical Inequalities and Chemical Applicability of PAHs

Chaluvaraju

2022

rrijm

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Topological indices are graphical invariants that relate a numeric number to a graph, which is structurally invariant and predicts the chemical, biological and physical features of the molecular graphs. In this work, mathematical inequalities of generalized second neighborhood Zagreb index are obtained. Further, generalized second neighborhood Zagreb indices for some particular values are computed for some basic polycyclic aromatic hydrocarbons, and the QSPR analysis are also obtained.

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“…is the degree sum of neighbour vertices of 𝑣 in 𝑉(𝐺). This descriptor is defined by [17] and studied by [18][19][20][21][22][23].…”

Section: 𝑢𝑣∈𝐸(𝐺)mentioning

confidence: 99%

Generalized Second Neighborhood Zagreb Index: Mathematical Inequalities and Chemical Applicability of PAHs

Chaluvaraju

2022

rrijm

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“…Graphene is denoted by G t,s , where t is the number of rows of benzene rings and s is the number of benzene rings in each row. Graphene has 2st + 2s + 2t vertices and 3st + 2s + 2t − 1 edges [33]. Figure 1 shows the graphene G t,s .…”

Section: Graphene Networkmentioning

confidence: 99%

Study of Graphene Networks and Line Graph of Graphene Networks via NM‐Polynomial and Topological Indices

Nazeer

Ahmed

et al. 2022

Journal of Mathematics

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The topological invariants are related to the molecular graph of the chemical structure and are numerical numbers that help us to understand the topology of the concerned chemical structure. With the help of these numbers, many properties of graphene can be guessed without preforming any experiment. Huge amount of calculations are required to obtain topological invariants for graphene, but by applying basic calculus roles, neighborhood M -polynomial of graphene gives its indices. The aim of this work is to compute neighborhood degree-dependent indices for the graph of graphene and the line graph of subdivision graph of graphene. Firstly, we establish neighborhood M-polynomial of these families of graphs, and then, by applying basic calculus, we obtain several neighborhood degree-dependent indices. Our results play an important role to understand graphene and enhance its abilities.

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“… 2019 Binu et al [ 8 ] They have introduced the connectivity index for fuzzy graphs. 2019 Mondal et al [ 26 , 27 ] They have introduced some neighbourhood degree based topological indices for crisp graphs. 2020 Binu et al [ 8 ] They have introduced the Wiener index for fuzzy graphs.…”

Section: Introductionmentioning

confidence: 99%

“…So this TI is very much useful in molecular chemistry, spectral graph theory, network theory, and several fields of mathematics and chemistry. Some neighbourhood degree-based topological indices are introduced and studied their correlations between the physico-chemical properties of some chemical compounds by Mondal et al [ 26 , 27 ]. In [ 29 ] they also studied neighbourhood Zagreb index of product graph and analyzed QSPR of some novel degree-based topological descriptors [ 30 ].…”

Section: Introductionmentioning

confidence: 99%

Further development of F-index for fuzzy graph and its application in Indian railway crime

Islam

Pal

2022

J. Appl. Math. Comput.

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From the mid-nineteenth century, the railway network has been the most important mode of conveying people and goods in India. 22.15 million passengers used this network and 3.32 million metric tons of goods were also shipped daily from 2019 to 2020. The national rail network comprised 126,366 km of track over a route of 67,368 km and 7,325 stations. It is the fourth-largest national railway network globally after the United States, Russia and China. But with the passage, they pose a threat to the general public while travelling, being the instances of crimes rising fourfold in rails. The ongoing railway crime has become a cause of concern for the common passenger now. In this article, F-index for fuzzy graphs is used to analyze the railway crimes in India and compared with three other topological indices. F-index for fuzzy graphs and the first Zagreb index for fuzzy graphs provide similar results whereas F-index for fuzzy graphs provides better realistic results than F-index for crisp graphs and first Zagreb index for crisp graphs to detect the crime in Indian railway. Also, this index is studied for several operations such as Cartesian product, composition, union and join of two fuzzy graphs. Some interesting relations of F-index are established during fuzzy graph transformations. Using those transformation, it is shown that n -vertex star has maximum F-index among the n -vertex trees. Also, maximal n -vertex unicyclic fuzzy graph having r cycle is determined with respect to F-index.

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Topological properties of Graphene using some novel neighborhood degree-based topological indices

Cited by 37 publications

References 14 publications

Generalized Second Neighborhood Zagreb Index: Mathematical Inequalities and Chemical Applicability of PAHs

Generalized Second Neighborhood Zagreb Index: Mathematical Inequalities and Chemical Applicability of PAHs

Study of Graphene Networks and Line Graph of Graphene Networks via NM‐Polynomial and Topological Indices

Further development of F-index for fuzzy graph and its application in Indian railway crime

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