On the Upper Bounds of Fractional Metric Dimension of Symmetric Networks

Javaid, Muhammad; Aslam, Muhammad; Liu, Jia‐Bao

doi:10.1155/2021/8417127

Cited by 3 publications

(5 citation statements)

References 21 publications

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“…This section is dedicated to the construction of the networks under consideration. As defined in [19], for m ≥ a quadrangular circular ladder (QCL) Q 1 m is a cubic network that is the network obtained after the Cartesian product of P 2 × C m . A subdivided QCL denoted by SQ m is formed after applying the subdivision operation on QCL by adding vertex x s between vertices v s and v s+1 , y s between vertices v s and w s and z s between vertices w s and w s+1 .…”

Section: Construction Of Web-related Networkmentioning

confidence: 99%

“…The 2-faced web network WB 1 m is formed by joining vertices z s to the vertices y s of 2-faced QCL as defined in [19]. Its order is 3m and size is 4m.…”

Section: Construction Of Web-related Networkmentioning

confidence: 99%

“…Its V(WB 1 m ) and E(WB 1 m ) are given as follows: It is clear from Figure 2 that WB 1 m is a bipartite network. The 3-faced web networks WB 2 m and WB 3 m are formed by joining vertices z s to the vertices y s of 3-faced QCLs Q 2 m and Q 3 m as defined in [19]. Their order is 3m and size is 5m.…”

Section: Construction Of Web-related Networkmentioning

confidence: 99%

“…Afterwards, researchers have stormed with the results of FMD of networks, which are the resultants of various graph operations such as comb, corona, Cartesian, hierarchical, and lexicographic products, see [13][14][15][16]. Similarly, the FMDs of the generalized Jahangir network, metal organic networks, rotationally symmetric and planar networks, tetrahedral diamond and grid-like networks can be found in [17][18][19][20][21]. Moreover, for improved lower bound of FMD and bounds of FMD of convex polytopes, see [22].…”

Section: Introductionmentioning

confidence: 99%

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Lower and Upper Bounds of Fractional Metric Dimension of Connected Networks

et al. 2021

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The distance centric parameter in the theory of networks called by metric dimension plays a vital role in encountering the distance-related problems for the monitoring of the large-scale networks in the various fields of chemistry and computer science such as navigation, image processing, pattern recognition, integer programming, optimal transportation models and drugs discovery. In particular, it is used to find the locations of robots with respect to shortest distance among the destinations, minimum consumption of time, lesser number of the utilized nodes, and to characterize the chemical compounds, having unique presentations in molecular networks. After the arrival of its weighted version, known as fractional metric dimension, the rectification of distance-related problems in the aforementioned fields has revived to a great extent. In this article, we compute fractional as well as local fractional metric dimensions of web-related networks called by subdivided QCL, 2-faced web, 3-faced web, and antiprism web networks. Moreover, we analyse their final results using 2D and 3D plots.

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Section: Construction Of Web-related Networkmentioning

confidence: 99%

“…The 2-faced web network WB 1 m is formed by joining vertices z s to the vertices y s of 2-faced QCL as defined in [19]. Its order is 3m and size is 4m.…”

Section: Construction Of Web-related Networkmentioning

confidence: 99%

Section: Construction Of Web-related Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lower and Upper Bounds of Fractional Metric Dimension of Connected Networks

et al. 2021

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“…Integer Programming, where the goal is to discover integer solutions that optimize a particular criterion [37]. • Chemistry and Drug Discovery, where metric dimension is used in molecular networks and chemical compound analysis to characterize and describe chemical compounds in a distinctive way, assisting in the identification of novel medications or comprehending chemical interactions [38].…”

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confidence: 99%

On Sharp Bounds of Local Fractional Metric Dimension for Certain Symmetrical Algebraic Structure Graphs

Alali,

Ali,

Adnan

et al. 2023

Symmetry

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The smallest set of vertices needed to differentiate or categorize every other vertex in a graph is referred to as the graph’s metric dimension. Finding the class of graphs for a particular given metric dimension is an NP-hard problem. This concept has applications in many different domains, including graph theory, network architecture, and facility location problems. A graph G with order n is known as a Toeplitz graph over the subset S of consecutive collections of integers from one to n, and two vertices will be adjacent to each other if their absolute difference is a member of S. A graph G(Zn) is called a zero-divisor graph over the zero divisors of a commutative ring Zn, in which two vertices will be adjacent to each other if their product will leave the remainder zero under modulo n. Since the local fractional metric dimension problem is NP-hard, it is computationally difficult to identify an optimal solution or to precisely determine the minimal size of a local resolving set; in the worst case, the process takes exponential time. Different upper bound sequences of local fractional metric dimension are suggested in this article, along with a comparison analysis for certain families of Toeplitz and zero-divisor graphs. Furthermore, we note that the analyzed local fractional metric dimension upper bounds fall into three metric families: constant, limited, and unbounded.

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Generalized perimantanes diamondoid structure and their edge-based metric dimensions

Ahmad

2022

MATH

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<abstract><p>Due to its superlative physical qualities and its beauty, the diamond is a renowned structure. While the green-colored perimantanes diamondoid is one of a higher diamond structure. Motivated by the structure's applications and usage, we look into the edge-based metric parameters of this structure. In this draft, we have discussed edge metric dimension and their generalizations for the generalized perimantanes diamondoid structure and proved that each parameter depends on the copies of original or base perimantanes diamondoid structure and changes with the parameter $ {\lambda} $ or its number of copies.</p></abstract>

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On the Upper Bounds of Fractional Metric Dimension of Symmetric Networks

Cited by 3 publications

References 21 publications

Lower and Upper Bounds of Fractional Metric Dimension of Connected Networks

Lower and Upper Bounds of Fractional Metric Dimension of Connected Networks

On Sharp Bounds of Local Fractional Metric Dimension for Certain Symmetrical Algebraic Structure Graphs

Generalized perimantanes diamondoid structure and their edge-based metric dimensions

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