Anwar Alwardi

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Papers by Anwar Alwardi

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

Open Journal of Applied Sciences, 2021

A graphical index is a numeric value corresponding to a graph which is structurally invariant and... more 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 M dn -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.

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On the Vector Degree Matrix of a Connected Graph

Journal of Mathematics, 2022

A matrix representation of the graph is one of the tools to study the algebraic structure and pro... more A matrix representation of the graph is one of the tools to study the algebraic structure and properties of a graph. In this paper, by defining the vector degree matrix of graph G, we provide a new matrix representation of the graph. For some standard graphs, VD-eigenvalues, VD-spectrum, and VD-energy values are defined and calculated. Moreover, we calculate the VD-matrix and calculate the VD-eigenvalues for graphs representing the chemical composition of paracetamol and tramadol.

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Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program

Proyecciones, Mar 11, 2024

A topological index is a branch of chemical graph theory that is vital to analyzing the physio-ch... more A topological index is a branch of chemical graph theory that is vital to analyzing the physio-chemical characteristics of chemical compound structures divided into a degree-based molecular structure such as Zagreb indices, a distance-based molecular structure such as Wiener index, and a mixed such as Gutman index. In this paper, some definitions, results, and examples of Wiener polynomial and index for subdivision graph of friendship, and bifriendship graphs, line subdivision graph of friendship, and bifriendship graphs were introduced. Moreover, we used the MATLAB program to calculate the Wiener polynomial and index of these graphs and refer to some applications.

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Distance Eccentric Connectivity Index of Graphs

On Vn-Arithmetic Graph

International journal of computer applications, Sep 17, 2015

V n -Arithmetic graph has been introduced by Vasumathi and Vangipuram [9]. In this paper some pro... more V n -Arithmetic graph has been introduced by Vasumathi and Vangipuram [9]. In this paper some properties of V n -Arithmetic graph, maximum degree, minimum degree, number of edges, diameter, radius, Hamiltonian and Eulerian are studied. Also, we introduce m-Arithmetical graphs. Some properties and interesting results for m-Arithmetical graphs are established.

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Edge injective domination of graphs

Gulf Journal of Mathematics, Jun 14, 2017

Let G = (V, E) be a simple graph. A subset X of E is called edge injective dominating set (edge I... more Let G = (V, E) be a simple graph. A subset X of E is called edge injective dominating set (edge Inj-dominating set) if for every edge f ∈ E -X there exists an edge g ∈ X such that |Γ(f, g)| ≥ 1, where |Γ(f, g)| is the number of common edge neighbors between the edges f and g. The minimum cardinality of such edge dominating set denoted by γ in (G) and is called edge injective domination number (edge Inj-domination number) of G. In this paper, we introduce the edge injective domination number, injective independence edge number (Inj-independence edge number) β in (G) and edge injective domatic number (edge Inj-domatic number) d in (G) of a graph G. Exact values for some standard graphs, bounds and some interesting results are established.

format_quoteIntroduced edge injective domination number, injective independence edge number, and related concepts for standard graphs.format_quote

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On Designs arising from Corona Product H ◦ K3

IOSR journal of mathematics, May 1, 2016

In this paper, we determine the partially balanced incomplete block designs and association schem... more In this paper, we determine the partially balanced incomplete block designs and association scheme which are formed by the minimum dominating sets of the graphs C 3 • K 3 , we determine the number of minimum dominating sets of graph G = C n • K 3 and prove that the set of all mini-mum dominating sets of G = C n •K 3 forms a partially balanced incomplete block design with two association scheme. Finally we generalize the results for the graph H • K 3 .

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Connected Equitable Domination in Graphs

Let G = (V, E) be a graph. A subset D of V is called an equitable dominating set of a graph G if ... more Let G = (V, E) be a graph. A subset D of V is called an equitable dominating set of a graph G if for every v ∈ V -D, there exists a vertex v ∈ D such that uv ∈ E(G) and |deg(u)deg(v)| ≤ 1, where deg(u) is the degree of u and deg(v) is the degree of v in G. An equitable dominating set D is said to be a connected equitable dominating set if the subgraph D induced by D is connected. The minimum of the cardinalities of the connected equitable dominating sets of G is called the connected equitable domination number and denoted by γ ce (G) In this paper we introduce the connected equitable domination and connected equitable domatic in a graph, bounds for γ ce (G), d ce (G) and its exact values for some standard graphs are found.

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Independent injective domination of graphs

DOAJ (DOAJ: Directory of Open Access Journals), Jul 1, 2016

An injective dominating set S in a graph G is called independent injective dominating set (IInj-d... more An injective dominating set S in a graph G is called independent injective dominating set (IInj-dominating set) if for every v ∈ S, N (v) ∩ S = φ. The minimum cardinality of such injective dominating set is called independent injective domination number of G and denoted by γ i i n (G). In this paper, we introduce the independent injective domination of graphs and we define the IID-graph. Exact values for some families of graphs, relations with the other domination parameters are obtained. Also, we introduce the independent injective frustration number of graphs. Bounds and some interesting results are established.

Domination, gamma-Domination Topological Indices and phi(P)-Polynomial of Some Chemical Structures Applied for the Treatment of COVID-19 Patients

Biointerface Research in Applied Chemistry, 2021

In medical science, pharmacology, chemical, biological, pharmaceutical properties of molecular st... more In medical science, pharmacology, chemical, biological, pharmaceutical properties of molecular structure are essential for drug preparation and design. These properties can be studied by using topological indices calculation. In this research work, we establish the topological properties of some chemical structures that have been applied for the treatment of COVID-19 patients by using the domination of topological indices and γ -domination indices. We determine the φ Ppolynomial for the antiviral chemical structures. The results obtained can help study the chemical properties of chemical structures that have been applied for the treatment of COVID-19 patients.

format_quoteResults from topological indices for chloroquine were analyzed using harmonic arithmetic and analytical methods, improving insight into drug structures' properties.format_quote

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Domination topological properties of polyhydroxybutyrate and polycaprolactone with QSPR analysis

Nanosystems: Physics, Chemistry, Mathematics, 2021

Polyhydroxyalkanoates (PHAs) are biopolymers, which are stored inside cells as energy storage mat... more Polyhydroxyalkanoates (PHAs) are biopolymers, which are stored inside cells as energy storage materials by various microorganisms. PHAs are plastic materials that have a positive environmental impact when compared to regular plastics in terms of production methods and recyclabillity. In addition, PHAs are characterized by biocompatibility, biodegradability and thus have a wide range of applications such as biomedicine, surgery, etc. The most common PHAs are Polyhydroxybutyrate, Polyhydroxyvalerate, and copolymer. In this paper, we calculate the domination topological indices of these polymers; also, we discuss the quantitative structure property relationships (QSPR) analysis of these domination topological indices. Further, we show that the characteristics have a good correlation with the physico-chemical characteristics of polymers.

An Atlas of Different Distances Sets Polynomials of Graphs of Order at Most Six

On the Uphill Zagreb Indices of Graphs

International Journal of Analysis and Applications, 2022

One of the tools, to research and investigation the structural dependence of various properties a... more One of the tools, to research and investigation the structural dependence of various properties and some activities of chemical structures and networks is the topological indices of graphs. In this research work, we introduce novel indices of graphs which they based on the uphill degree of the vertices termed as uphill Zagreb topological indices. Exact formulae of these new indices for some important and famous families of graphs are established.

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Downhill Zagreb Topological Indices of Graphs

International Journal of Analysis and Applications, 2021

Topological indices are graph invariants determined by the distance or degree of vertices of the ... more Topological indices are graph invariants determined by the distance or degree of vertices of the molecular graph. Topological indices have been used effectively in chemical graph theory in explaining the structures and predicting certain physicochemical properties of chemical compounds. In this research, we introduce the first, second, and forgotten downhill Zagreb indices and calculate those topological indices for some standard families of graphs and the join of graphs. Also, the downhill topological indices for the firefly graph, book graph, and stacked book graph are established. Finally, the downhill indices of Graphene and honeycomb network are obtained.

format_quoteTopological indices correlate chemical constitution with physical properties, chemical reactivity, and biological activity, showcasing their utility in documentation.format_quote

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Independent Dominating Polynomial in Graphs

Abstract: Let , G V E be a graph of order n. The independent domination polynomial of G is the po... more

HDR Degree Bassed Indices and Mhr-Polynomial for the Treatment of COVID-19

Biointerface Research in Applied Chemistry, 2021

In this research work, We introduce topological indices, namely as an HDR version of Modified Zag... more In this research work, We introduce topological indices, namely as an HDR version of Modified Zagreb topological index (HDRM*), HDR version of Modified forgotten topological index (HDRF*), and HDR version of hyper Zagreb index (HDRHM*). Then the relatively study depends on the structure-property regression analysis to test and compute the chemical applicability of these indices to predict the physicochemical properties of octane isomers. Also, we show these HDR indices have well degeneracy properties compared to other degree-based topological indices. Also, We defined and computed the Mhr-polynomial of the newly indices and applied it on COVID-19 treatments. Also, we discussed some mathematical properties of HDR indices.

format_quoteAntiviral agents tested reduced COVID-19 recovery time, with remdesivir receiving FDA emergency approval, highlighting real-world applications.format_quote

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