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Downhill Zagreb Topological Indices and <i>M<SUB>dn</SUB></i>-Polynomial of Some Chemical Structures Applied for the Treatment of COVID-19 Patients

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Open Journal of Applied Sciences 2021年第4期10卷 395-413页

作者： Bashair Al-Ahmadi Anwar Saleh wafa Al-shammakh Department of Mathematics Faculty of Science University of Jeddah Jeddah Saudi Arabia

A graphical index is a numeric value corresponding to a graph which is structurally invariant and in molecular graph theory these invariants are known as topological indices. In the field of Chemical and Medical Sciences, the topological indices are used to study the chemical, biological, medical and pharmaceutical features of drugs. With reference to the previous deadly diseases, the COVID-19 pandemic has considered to be the biggest life threatening issue that modern medicines have ever tackled. COVID-19 is immedicable and even the existing treatments are only helping the certain group of sufferers. Scientists have tested available antiviral agents and got a favorable impact on recovering from pandemic. Some of these antiviral agents are remdesivir, chloroquine, hydroxychloroquine, theaflavin and dexamethasone. Keeping in view of the importance of topological indices in the study of pharmaceutical and chemical drugs, in this paper, we calculate the Mdn-Polynomial, some downhill Zagreb topological indices and some downhill Zagreb polynomials of some of the anti viral agents remdesivir, chloroquine, hydroxychloroquine, theaflavin and dexamethasone. The results thus obtained may be useful for the finding new medicine and vaccine for the treatment of COVID-19.

关键词： COVID-19 Remdesivir Chloroquine Hydroxychloroquine Theaflavin Dexamethasone Mdn-Polynomial Downhill Zagreb Polynomial

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Numerical Solutions for Quadratic Integro-Differential Equations of Fractional Orders

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Open Journal of Applied Sciences 2017年第4期7卷 157-170页

作者： Fatheah Alhendi wafa shammakh Hind Al-Badrani Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia Taibah University Madinah Saudi Arabia

In this article, variational iteration method (VIM) and homotopy perturbation method (HPM) solve the nonlinear initial value problems of first-order fractional quadratic integro-differential equations (FQIDEs). We use the Caputo sense in this article to describe the fractional derivatives. The solutions of the problems are derived by infinite convergent series, and the results show that both methods are most convenient and effective.

关键词： Fractional Quadratic Integro-Differential Equations Variational Iteration Method Homotopy Perturbation Method

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On the Uphill Domination Polynomial of Graphs

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Journal of Applied Mathematics and Physics 2020年第6期8卷 1168-1179页

作者： Thekra Alsalomy Anwar Saleh Najat Muthana wafa Al shammakh Department of Mathematics Faculty of Science University of Jeddah Jeddah Saudi Arabia

A path π = [v1, v2, …, vk] in a graph G = (V, E) is an uphill path if deg(vi) ≤ deg(vi+1) for every 1 ≤ i ≤ k. A subset S ⊆ V(G) is an uphill dominating set if every vertex vi ∈ V(G) lies on an uphill path originating from some vertex in S. The uphill domination number of G is denoted by γup(G) and is the minimum cardinality of the uphill dominating set of G. In this paper, we introduce the uphill domination polynomial of a graph G. The uphill domination polynomial of a graph G of n vertices is the polynomial , where up(G, i) is the number of uphill dominating sets of size i in G, and γup(G) is the uphill domination number of G, we compute the uphill domination polynomial and its roots for some families of standard graphs. Also, UP(G, x) for some graph operations is obtained.

关键词： Domination Uphill Domination Uphill Domination Polynomial

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