Computing the edge metric dimension of convex polytopes related graphs

Ahsan, Muhammad; Zahid, Zohaib; Zafar, Sohail; Rafiq, Arif; Sindhu, Muhammad Sarwar; Umar, Muhammad Awais

doi:10.22436/jmcs.022.02.08

Cited by 35 publications

(19 citation statements)

References 13 publications

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“…Koam and Ahmad [15] studied edge metric dimension of barycentric subdivision of Cayley graph. e convex polytope graph was discussed by Zhang and Gao in [16] and Ahsan et al in [17]. Yang et al discussed some chemical structures related to wheel graphs in [18].…”

Section: Introductionmentioning

confidence: 99%

On the Edge Metric Dimension of Different Families of Möbius Networks

Deng

Nadeem

Azeem

2021

Mathematical Problems in Engineering

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For an ordered subset Q e of vertices in a simple connected graph G , a vertex x ∈ V distinguishes two edges e 1 , e 2 ∈ E , if d x , e 1 ≠ d x , e 2 . A subset Q e having minimum vertices is called an edge metric generator for G , if every two distinct edges of G are distinguished by some vertex of Q e . The minimum cardinality of an edge metric generator for G is called the edge metric dimension, and it is denoted by dim e G . In this paper, we study the edge resolvability parameter for different families of Möbius ladder networks and we find the exact edge metric dimension of triangular, square, and hexagonal Möbius ladder networks.

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Section: Introductionmentioning

confidence: 99%

On the Edge Metric Dimension of Different Families of Möbius Networks

Deng

Nadeem

Azeem

2021

Mathematical Problems in Engineering

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“…Many authors have introduced and analyzed certain variations of resolving sets, such as local resolving set, partition resolving set, fault-tolerant resolving set, resolving dominating set, strong resolving set, independent resolving set, and so on. For further details the reader is referred to [1,6,10,21,22,32,33]. In addition to defining other variants of resolving sets in graphs, Kelenc et al [22], introduced a parameter used to uniquely distinguish graph edges and called it the edge metric dimension.…”

Section: Introductionmentioning

confidence: 99%

Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone

2021

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Minimum resolving sets (edge or vertex) have become an integral part of molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the network, uniquely. The distance between an edge e = cz and a vertex u is defined by d(e, u) = min{d(c, u), d(z, u)}. If d(e1, u) ≠ d(e2, u), then we say that the vertex u resolves (distinguishes) two edges e1 and e2 in a connected graph G. A subset of vertices RE in G is said to be an edge resolving set for G, if for every two distinct edges e1 and e2 in G we have d(e1, u) ≠ d(e2, u) for at least one vertex u ∈ RE. An edge metric basis for G is an edge resolving set with minimum cardinality and this cardinality is called the edge metric dimension edim(G) of G. In this article, we determine the edge metric dimension of one-pentagonal carbon nanocone (1-PCNC). We also show that the edge resolving set for 1-PCNC is independent.

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“…The VC 5 C 7 nano-tubes and structure of H-Naphtalenic are studied in [18], sharps bounds are computed for the network of cellulose with respect to distance based graph theoretical parameters in [19], α-boron nanotubes derived from two dimensional lattice are studied in [20], and also provide some links for its applications, [21] computed the distance-based metric for the silicate star. Moving towards the edge metric dimension, barycentric subdivision of Cayley graph studied in [22], few work on the convex polytopes structure discussed by [23,24], the wheel graphs related chemical structures are discussed in [25] and a quantitative review between metric its other versions is done in [26], moreover, the seminal work on the edge metric dimension can be found in [27]. The renowned chemical topology of polycyclic aromatic hydrocarbons are discussed in [28], with the conceptualization of resolvability parameters.…”

Section: Introductionmentioning

confidence: 99%

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

et al. 2021

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Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.

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Computing the edge metric dimension of convex polytopes related graphs

Cited by 35 publications

References 13 publications

On the Edge Metric Dimension of Different Families of Möbius Networks

On the Edge Metric Dimension of Different Families of Möbius Networks

Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

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