Computation of Metric-Based Resolvability of Quartz Without Pendant Nodes

Koam, Ali N. A.; Ahmad, Ali; Alatawi, Maryam Salem; Nadeem, Muhammad Faisal; Azeem, Muhammad

doi:10.1109/access.2021.3126455

Cited by 5 publications

(4 citation statements)

References 44 publications

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“…Harary and Melter independently discovered the ideas of a metric basis as a minimum resolving set of 𝐺 and the cardinality of 𝐵 as a metric dimension [5]. A number of graphs' metric dimensions are found in [6][7][8][9][10][11][12][13][14][15]. The following are the graphs: corona product [6], regular bipartite [7], chain graphs [8], mobius ladder [9], circulant graphs and Cayley hypergraphs [10], heptagonal circular ladder [11], generalized Petersen multigraphs [12], power of total graph [13], friendship graph [14], and quartz graph [15].…”

Section: Introductionmentioning

confidence: 99%

“…A number of graphs' metric dimensions are found in [6][7][8][9][10][11][12][13][14][15]. The following are the graphs: corona product [6], regular bipartite [7], chain graphs [8], mobius ladder [9], circulant graphs and Cayley hypergraphs [10], heptagonal circular ladder [11], generalized Petersen multigraphs [12], power of total graph [13], friendship graph [14], and quartz graph [15]. Specifically, the authors in [1] studied the linked metric dimension of the 𝑛 − 1 star network 𝐾 , full graph 𝐾 , cycle graph 𝐶 , route graph 𝑃 , and wheel graph 𝑊 .…”

Section: Introductionmentioning

confidence: 99%

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Connected metric dimension of the class of ladder graphs

Batiha,

Amin,

Mohamed

et al. 2024

Math. models, eng.

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Numerous applications, like robot navigation, network verification and discovery, geographical routing protocols, and combinatorial optimization, make use of the metric dimension and connected metric dimension of graphs. In this work, the connected metric dimension types of ladder graphs, namely, ladder, circular, open, and triangular ladder graphs, as well as open diagonal and slanting ladder graphs, are studied.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Connected metric dimension of the class of ladder graphs

Batiha,

Amin,

Mohamed

et al. 2024

Math. models, eng.

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“…The metric dimension of several graphs is computed theoretically in the literature [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A few algorithms are proposed in the literature to compute the metric dimension of graphs heuristically.…”

Section: Introductionmentioning

confidence: 99%

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

Mohamed¹,

Mohaisen²,

Amin³

2023

Intelligent Automation &Amp; Soft Computing

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In this paper, we consider the NP-hard problem of finding the minimum connected resolving set of graphs. A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set B of G is connected if the subgraph B induced by B is a nontrivial connected subgraph of G. The cardinality of the minimal resolving set is the metric dimension of G and the cardinality of minimum connected resolving set is the connected metric dimension of G. The problem is solved heuristically by a binary version of an enhanced Harris Hawk Optimization (BEHHO) algorithm. This is the first attempt to determine the connected resolving set heuristically. BEHHO combines classical HHO with opposition-based learning, chaotic local search and is equipped with an S-shaped transfer function to convert the continuous variable into a binary one. The hawks of BEHHO are binary encoded and are used to represent which one of the vertices of a graph belongs to the connected resolving set. The feasibility is enforced by repairing hawks such that an additional node selected from V\B is added to B up to obtain the connected resolving set. The proposed BEHHO algorithm is compared to binary Harris Hawk Optimization (BHHO), binary opposition-based learning Harris Hawk Optimization (BOHHO), binary chaotic local search Harris Hawk Optimization (BCHHO) algorithms. Computational results confirm the superiority of the BEHHO for determining connected metric dimension.

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“…Further study on partition dimension can be seen in [11,12]. In 2015, Moreno et al [13] presented the concept of κ− metric.…”

Section: Introductionmentioning

confidence: 99%

Fault Tolerant Partition Resolvability in Convex Polytopes

Nadeem

Kashif

Bonyah

et al. 2022

Mathematical Problems in Engineering

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Convex polytopes are special types of polytopes having an additional property that they are also convex sets in the n-dimensional Euclidean space. The convex polytope topologies are being used in the antitracking networks due to their stability, resilience, and destroy-resistance. The metric related parameters have been extensively studied in the recent times due to their applications in several areas including robot navigation, network designing, image processing, and chemistry. In this article, the sharp bounds for the fault tolerant partition dimension of certain well-known families of convex polytopes Rn, Qn, Sn, Tn, and Dn have been computed. Furthermore, we have studied the graphs having fault tolerant partition dimension bounded below by 4.

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Computation of Metric-Based Resolvability of Quartz Without Pendant Nodes

Cited by 5 publications

References 44 publications

Connected metric dimension of the class of ladder graphs

Connected metric dimension of the class of ladder graphs

Computing Connected Resolvability of Graphs Using Binary Enhanced Harris Hawks Optimization

Fault Tolerant Partition Resolvability in Convex Polytopes

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