Topological indices of the subdivision of a family of partial cubes and computation of $$\hbox {SiO}_2$$ related structures

Arockiaraj, Micheal; Klavžar, Sandi; Mushtaq, Shagufa; Balasubramanian, K.

doi:10.1007/s10910-019-01043-y

Cited by 13 publications

(11 citation statements)

References 23 publications

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“…A number of researchers reported their research results on topical drug diffusion problem in the dermal layer in human body [1][2][3][4][5][6][7][8][9][10]. Some of them use the molecular nanotechnology point of view [11][12][13][14]. In line with them, Sharma and Saxena [15] worked on finite element modelling in transdermal delivery system of drug especially when the case is at the steady state condition.…”

Section: Introductionmentioning

confidence: 99%

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

Mungkasi

2021

ARFMTS

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We consider the problem of drug diffusion in the dermal layer of human body. Two existing mathematical models of the drug diffusion problem are recalled. We obtain that the existing models lead to inconsistent equations for the steady state condition. We also obtain that solutions to the existing models are unrealistic for some cases of the unsteady state condition, because negative drug concentrations occur due to the inappropriate assumption of the model. Therefore, in this paper, we propose a modified mathematical model, so that the model is consistent, and the solution is nonnegative for both steady and unsteady state conditions of the drug diffusion problem in the dermal layer of human body. For the steady state condition, the exact solution to the proposed model is given. For unsteady state condition, we use a finite difference method for solving the models numerically, where the discretisation is centred in space and forward in time. Simulation results confirm that our proposed model and method preserve the non-negativity of the solution to the problem, so the solution is more realistic than that of the old model.

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Section: Introductionmentioning

confidence: 99%

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

Mungkasi

2021

ARFMTS

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“…As already mentioned, a cut method was applied on various Szeged‐like topological indices. For example, see recent papers on Szeged indices [27], weighted Szeged and PI indices [29], Mostar indices and weighted Mostar indices [30–32], and different distance‐based topological indices [33–35]. In this paper, we greatly generalize these results by introducing the concept of a general Szeged‐like topological index, which includes all the mentioned indices and also infinitely many other topological indices that can be defined in a similar way.…”

Section: Introductionmentioning

confidence: 80%

General cut method for computing Szeged‐like topological indices with applications to molecular graphs

Brezovnik

Tratnik

2020

Int J of Quantum Chemistry

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Szeged, PI and Mostar indices are some of the most investigated distance‐based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called Szeged‐like topological indices. In this paper, we formally introduce the concept of a general Szeged‐like topological index, which includes all mentioned indices and also infinitely many other topological indices that can be defined in a similar way. As the main result of the paper, we provide a cut method for computing a general Szeged‐like topological index for any strength‐weighted graph. This greatly generalizes various methods known for some of the mentioned indices and therefore rounds off such investigations. Moreover, we provide applications of our main result to benzenoid systems, phenylenes, and coronoid systems, which are well‐known families of molecular graphs. In particular, closed‐form formulas for some subfamilies of these graphs are deduced.

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“…In [12] formulas were proved for the Mostar index of Cartesian products in which both factors are paths or both factors are partial cubes. (See [5,7,23,24] for recent investigations of partial cubes.) A formula for the Mostar index of arbitrary Cartesian products was then independently given in [2,Theorem 1.5] and in [21,Theorem 3.1].…”

Section: Cartesian Productmentioning

confidence: 99%

On the Mostar index of trees and product graphs

Alizadeh

Klavžar

2021

Filomat

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If G is a graph, and if for e = uv ? E(G) the number of vertices closer to u than to v is denoted by nu, then Mo(G) = ? uv?E(G) |nu-nv| is the Mostar index of G. In this paper, the Mostar index is studied on trees and graph products. Lower and upper bounds are given on the difference between the Mostar indices of a tree and a tree obtained by contraction one of its edges and the corresponding extremal trees are characterized. An upper bound on the Mostar index for the class of all trees but the stars is proved. Extremal trees are also determined on the (k+1)-th largest/smallest Mostar index. The index is also studied on Cartesian and corona products.

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Topological indices of the subdivision of a family of partial cubes and computation of $$\hbox {SiO}_2$$ related structures

Cited by 13 publications

References 23 publications

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

Modelling And Simulation of Topical Drug Diffusion in The Dermal Layer of Human Body

General cut method for computing Szeged‐like topological indices with applications to molecular graphs

On the Mostar index of trees and product graphs

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