Partition dimension of COVID antiviral drug structures

Khabyah, Ali Al; Jamil, Muhammad Kamran; Koam, Ali N. A.; Javed, Aisha; Azeem, Muhammad

doi:10.3934/mbe.2022471

Cited by 5 publications

(4 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Resolvability of the graph has application in many fields of science such as in chemistry for representing chemical compounds (Browsable, 1998), Djokovic-Winkler relation (Caceres et al, 2007), strategies for the mastermind game (Chvatal, 1983), pattern recognition and image processing, hierarchical data structures (Melter and Tomescu, 1984), and robots navigation in networks (Khuller et al, 1994). For a better understanding of this topic, some very detailed articles are (Chartrand et al, 2000b;Saenpholphat and Zhang, 2002;Javaid et al, 2012;Velazquez et al, 2012;Velázquez et al, 2014;Yero et al, 2014;Siddiqui and Imran, 2015;Alatawi et al, 2022;Alshehri et al, 2022;Khabyah et al, 2022;Koam et al, 2022,a,b;Nadeem et al, 2022).…”

Section: Figurementioning

confidence: 99%

Computing the partition dimension of certain families of Toeplitz graph

Luo

Khalil²,

Ahmad

et al. 2022

Front. Comput. Neurosci.

View full text Add to dashboard Cite

Let G = (V(G), E(G)) be a graph with no loops, numerous edges, and only one component, which is made up of the vertex set V(G) and the edge set E(G). The distance d(u, v) between two vertices u, v that belong to the vertex set of H is the shortest path between them. A k-ordered partition of vertices is defined as β = {β1, β2, …, βk}. If all distances d(v, βk) are finite for all vertices v ∈ V, then the k-tuple (d(v, β1), d(v, β2), …, d(v, βk)) represents vertex v in terms of β, and is represented by r(v|β). If every vertex has a different presentation, the k-partition β is a resolving partition. The partition dimension of G, indicated by pd(G), is the minimal k for which there is a resolving k-partition of V(G). The partition dimension of Toeplitz graphs formed by two and three generators is constant, as shown in the following paper. The resolving set allows obtaining a unique representation for computer structures. In particular, they are used in pharmaceutical research for discovering patterns common to a variety of drugs. The above definitions are based on the hypothesis of chemical graph theory and it is a customary depiction of chemical compounds in form of graph structures, where the node and edge represent the atom and bond types, respectively.

show abstract

Section: Figurementioning

confidence: 99%

Computing the partition dimension of certain families of Toeplitz graph

Luo

Khalil²,

Ahmad

et al. 2022

Front. Comput. Neurosci.

View full text Add to dashboard Cite

show abstract

“…There are maany more graph theoretical parameters other than topological descriptors like resolvability parameters [ 29 – 42 ].…”

Section: Introductionmentioning

confidence: 99%

Valency-based structural properties of gamma-sheet of boron clusters

Koam,

Azeem,

Ahmad

2024

PLoS ONE

Self Cite

View full text Add to dashboard Cite

Boron cluster sheets are two-dimensional boron atom-based formations called borophene. They are similar to the two-dimensional sheet known as graphene, which is composed of carbon atoms arranged in a hexagonal lattice. The unique electrical, mechanical, and thermal properties of borophene make it a sought-after substance for a variety of uses, such as catalysis, energy storage, and electronics. There are two ways to manufacture borophene: chemical vapor deposition and molecular beam epitaxy. Vertex-edge valency-based topological descriptors are a great example of a molecular descriptor that provides information on the connection of atoms in a molecule. These descriptions are based on the notion that a node’s value in a molecular network is the sum of the valency of those atoms that are directly connected to that node. In this article, we discussed some novel vertex-edge (ve) and edge-vertex (ev) topological descriptors and found their formulations for the boron cluster or borophene sheets. Also, we show the numerical and graphical comparison of these descriptors in this article.

show abstract

“…The metric dimension of several graphs is computed theoretically in the literature [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A few algorithms are proposed in the literature to compute the metric dimension of graphs heuristically.…”

Section: Introductionmentioning

confidence: 99%

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

Mohamed¹,

Mohaisen²,

Amin³

2023

Intelligent Automation &Amp; Soft Computing

View full text Add to dashboard Cite

In this paper, we consider the NP-hard problem of finding the minimum connected resolving set of graphs. A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set B of G is connected if the subgraph B induced by B is a nontrivial connected subgraph of G. The cardinality of the minimal resolving set is the metric dimension of G and the cardinality of minimum connected resolving set is the connected metric dimension of G. The problem is solved heuristically by a binary version of an enhanced Harris Hawk Optimization (BEHHO) algorithm. This is the first attempt to determine the connected resolving set heuristically. BEHHO combines classical HHO with opposition-based learning, chaotic local search and is equipped with an S-shaped transfer function to convert the continuous variable into a binary one. The hawks of BEHHO are binary encoded and are used to represent which one of the vertices of a graph belongs to the connected resolving set. The feasibility is enforced by repairing hawks such that an additional node selected from V\B is added to B up to obtain the connected resolving set. The proposed BEHHO algorithm is compared to binary Harris Hawk Optimization (BHHO), binary opposition-based learning Harris Hawk Optimization (BOHHO), binary chaotic local search Harris Hawk Optimization (BCHHO) algorithms. Computational results confirm the superiority of the BEHHO for determining connected metric dimension.

show abstract

Partition dimension of COVID antiviral drug structures

Cited by 5 publications

References 51 publications

Computing the partition dimension of certain families of Toeplitz graph

Computing the partition dimension of certain families of Toeplitz graph

Valency-based structural properties of gamma-sheet of boron clusters

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

Contact Info

Product

Resources

About