Partition Dimension of Generalized Petersen Graph

Raza, Hassan; Liu, Jia‐Bao; Azeem, Muhammad; Nadeem, Muhammad

doi:10.1155/2021/5592476

Cited by 4 publications

(2 citation statements)

References 21 publications

(21 reference statements)

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“…Furthermore, it was studied that graphs having fault tolerant partition dimension are bounded below by 4. In [25], the authors considered the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets. In [17], the authors determined the partition dimension and strong metric dimension of a chain cycle constructed by even cycles and a chain cycle constructed by odd cycles [26] that mainly deal with metric dimension and partition dimension of tessellation of plane by boron nanosheets.…”

Section: Introductionmentioning

confidence: 99%

On Partition Dimension of Generalized Convex Polytopes

Shah,

Khan,

Ali

et al. 2023

Journal of Mathematics

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Let G be a graph having no loop or multiple edges, k − order vertex partition for G is represented by γ = γ 1 , γ 2 , … , γ k . The vector r ϕ γ = d ϕ , γ 1 , d ϕ , γ 2 , d ϕ , γ 3 ⋯ , d ϕ , γ k is the representation of vertex ϕ with respect to γ . If the representation of all the vertices with respect to γ is different, then γ is said to be resolving partition for the graph G . The minimum number k is resolving partition for G and is termed as partition dimension for G , represented by p d G . There are numerous applications of partition dimension in different fields such as optimization, computer, mastermind games, and networking and also in modeling of numerical structure. The problem of finding constant value of partition dimension for a graph or network is very hard, so one can find bounds for the partition dimension. In this work, we consider convex polytopes in their generalized forms that are E n , S n , and G n , and we compute upper bounds for the partition dimension of the desired polytopes.

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Section: Introductionmentioning

confidence: 99%

On Partition Dimension of Generalized Convex Polytopes

Shah,

Khan,

Ali

et al. 2023

Journal of Mathematics

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“…Literature on partition dimension and its bounds on the specifc families of graphs are found in [18,19]. Te antivirus properties of COVID structures are discussed in terms of partition dimension and bounds in [20], novel chemical structures of diamonded structures are discovered in [21] in terms of partition dimension bounds, carbon nanotube, and its partition dimension bounds are described in [22], hexagonal Mobius ladder networks are discussed in terms of bounds on the partition dimension in [23], Harary graphs are found in terms of partition dimension bounds in [24], alpha-boron nanotubes are available in [25], a novel chemical structure is found in terms of metric-based parameters in [26], and diferent generalised families of graphs are discussed in terms of resolving set and partition dimension in [27][28][29]. Defnition 1.…”

Section: Introductionmentioning

confidence: 99%

On the Bounded Partition Dimension of Some Generalised Graph Structures

Alghamdi

Asim²

2022

Journal of Mathematics

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Consider λ to be a connected graph with a vertex set V λ that may be partitioned into any partition set S . If each vertex in λ has a separate representation with regard to S and is an ordered k partition, then the set with S is a resolving partition of λ . . A partition dimension of λ , represented by p d , is the minimal cardinality of resolving k partitions of V λ . The partition dimension of various generalised families of graphs, such as the Harary graph, Cayley graph, and Pendent graph, is given as a sharp upper bound in this article.

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Finite vertex-based resolvability of supramolecular chain in dialkyltin

Zhang

Kanwal

Azeem

et al. 2022

Main Group Metal Chemistry

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For mammals, l-valine, which is a glycogen, is an essential amino acid. A protein made of 20 amino acids, salicylidene and l-valine make the carboxylate ligand which is the base of chiral Schiff. On a large scale, complexes with the ligand are utilized to help in the research work. To locate the exact location of a specific node from all the nodes, the entire node set is developed in a specific manner by choosing a particular subset and this subset is known as the resolving/locating set. This study contributed to the metric dimension of chemical complexes of supramolecular chain in dialkyltin from N-salicylidene-l-valine. We considered the complexes of 2,3,4 and ( C λ ⁎ ) ({C}_{\lambda }^{\ast }) chains and proved that the members of resolving sets are highly dependent on the number of vertices.

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Partition Dimension of Generalized Petersen Graph

Abstract: Let G = V G , … Show more

Cited by 4 publications

References 21 publications

On Partition Dimension of Generalized Convex Polytopes

On Partition Dimension of Generalized Convex Polytopes

On the Bounded Partition Dimension of Some Generalised Graph Structures

Finite vertex-based resolvability of supramolecular chain in dialkyltin

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