Sharp bounds on partition dimension of hexagonal Möbius ladder

Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Q a ⊂ V G is considered to be an adjacency metric generator for G if u 1 , u 2 ∈ V \ Q a (supposing each pair); there must exist a vertex q ∈ Q a along with the condition that q is indeed adjacent to one of u 1 , u 2 . The minimum number of elements in adjacency metric generator is the adjacency metric dimension of G , denoted by di m a G . In this work, we compute exact values of the adjacency metric dimension of circulant graph C n 1 , 2 , Möbius ladder, hexagonal Möbius ladder, and the ladder graph.

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“…It contains m-horizontal cycles of order four. For more study on ladder-type networks, see [30,31]. The metric dimension of ML m is three [32].…”

Section: Construction Of Graphsmentioning

confidence: 99%

On Adjacency Metric Dimension of Some Families of Graph

Koam

Ahmad

Azeem

et al. 2022

Journal of Function Spaces

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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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“…Drug discovery is not only a time-consuming process but also a costly process. In order to shorten this process, models that can predict the physicochemical and bioactivity properties of the newly produced molecular structure are obtained with topological indices studied in chemical mathematics [2][3][4][5][6]. Tese models are obtained via the structure-property/activity relationship (QSPR/QSAR) studies using molecular descriptors [7,8].…”

Section: Introductionmentioning

confidence: 99%

M‐Polynomial and NM‐Polynomial of Used Drugs against Monkeypox

Havare

Kamran

Bonyah³

2022

Journal of Mathematics

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Monkeypox has recently re-emerged. Since monkeypox has started to be seen in many countries without an epidemic, studies have started on new drugs used to treat this disease. Drug discovery is a challenging process. To alleviate this process, molecular descriptors used to predict the physical, chemical, and biological properties of chemical structures are studied. Molecular descriptors are numerical values of a chemical structure represented by a graph. In this study, M-polynomial and neighborhood M-polynomial molecular descriptors of drugs used and candidates for use in monkeypox are calculated and these descriptors are compared.

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Sharp bounds on partition dimension of hexagonal Möbius ladder

Cited by 58 publications

References 28 publications

On Adjacency Metric Dimension of Some Families of Graph

On Adjacency Metric Dimension of Some Families of Graph

Computing the partition dimension of certain families of Toeplitz graph

M‐Polynomial and NM‐Polynomial of Used Drugs against Monkeypox

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