Resolvability of the starphene structure and applications in electronics

Ahmad, Ali; Koam, Ali N. A.; Siddiqui, Mohammed Hakeem; Azeem, Muhammad

doi:10.1016/j.asej.2021.09.014

Cited by 30 publications

(21 citation statements)

References 39 publications

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“…The structure shown in the Figure 1 Metric dimension has many applied ways in which combinatorial optimization, robot roving, in complex games, in image processing, pharmaceutical chemistry, polymer industry, and in the electric field as well. All these applications are found in [4,24,41,48,50].…”

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confidence: 99%

RETRACTED: Vertex metric resolvability of COVID antiviral drug structures

Alqahtani

Jamil

Alshehri

et al. 2023

IFS

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In November of 2019 year, there was the first case of COVID-19 (Coronavirus) recorded, and up to 3 rd of April of 2020, 1,116,643 confirmed positive cases, and around 59,158 dying were recorded. Novel antiviral structures of the 2019 pandemic disease Coronavirus are discussed in terms of the metric basis of their molecular graph. These structures are named arbidol, chloroquine, hydroxy-chloroquine, thalidomide, and theaflavin. Metric dimension or metric basis is a concept in which the whole vertex set of a structure is uniquely identified with a chosen subset named as resolving set. Moreover, the fault-tolerant concept of those structures is also included in this study. By this concept of vertex-metric resolvability of COVID antiviral drug structures are uniquely identified and help to study the structural properties of the structure.

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confidence: 99%

RETRACTED: Vertex metric resolvability of COVID antiviral drug structures

Alqahtani

Jamil

Alshehri

et al. 2023

IFS

Self Cite

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“…They also came up with an exact solution for the parallel composition of pathways of various lengths. Some updated references are (Ahmad et al, 2021;Ali et al, 2021;Azeem et al, 2021Azeem et al, , 2022Shanmukha et al, 2022a,b,c;Usha 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.

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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.

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“…Edges Codes Edges Codes Edges Codes p 1,1 p 1,2 (0,13,14) q 1,6 q 1,7 (12,1,13)) r 2,3 r 2,4 (10,15,4) t 1,5 r 1,1 (11,2,11) p 1,2 p 1,3 (1,12,14) q 1,7 r 1,1 (13,0,13) r 2,4 r 2,5 (11,14,3) t 2,1 t 2,2 (8,15,6) p 1,3 p 1,4 (2,11,15) q 2,1 q 2,2…”

Section: Edgesunclassified

“…In vertices, p 1,i , p 2,i , q 1,j , q 2,j , r 1,k , and r 2,k , the indices i = 2b − 1, j = 2c − 1 and k = 2a − 1. Recently, results regarding vertex metric, edge metric, and mixed metric dimension of SP a,b,c have been reported due to Ahmad et al [1], which are as follows: Where pd(SP a,b,c ) is the partition dimension for SP a,b,c [6]. Next, motivated from these worth findings regarding some well-known resolvability parameters for SP a,b,c , we are interested to contribute more on this subject.…”

Section: Edgesmentioning

confidence: 99%

Multiset and Mixed Metric Dimension for Starphene and Zigzag-Edge Coronoid

Liu¹,

Sharma²,

Bhat³

et al. 2021

Preprint

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Let Γ = (V, E) be a simple connected graph. A vertex a is said to recognize (resolve) two different elements b 1 and bis said to be a mixed metric generator for Γ if each pair of distinct elements from V ∪ E are recognized by some element of U M . The mixed metric generator with a minimum number of elements is called a mixed metric basis of Γ. Then, the cardinality of this mixed metric basis for Γ is called the mixed metric dimension of Γ, denoted by mdim(Γ). The concept of studying chemical structures using graph theory terminologies is both appealing and practical. It enables researchers to more precisely and easily examines various chemical topologies and networks. In this paper, we consider two well known chemical structures; starphene SP a,b,c and six-sided hollow coronoid HC a,b,c and respectively compute their multiset dimension and mixed metric dimension. MSC(2020): 05C12, 05C90.

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Resolvability of the starphene structure and applications in electronics

Cited by 30 publications

References 39 publications

RETRACTED: Vertex metric resolvability of COVID antiviral drug structures

RETRACTED: Vertex metric resolvability of COVID antiviral drug structures

Computing the partition dimension of certain families of Toeplitz graph

Multiset and Mixed Metric Dimension for Starphene and Zigzag-Edge Coronoid

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