On minimum metric dimension of honeycomb networks

Manuel, Paul; Rajan, Bharati; Rajasingh, Indra; M, Chris Monica

doi:10.1016/j.jda.2006.09.002

Cited by 114 publications

(79 citation statements)

References 9 publications

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“…In light of these results, the complexity of Locating-Dominating Set and Metric Dimension for interval and permutation graphs is a natural open question (as posed in [28] and [11] for Metric Dimension on interval graphs), since these classes are standard candidates for designing ecient algorithms.…”

Section: Metric Dimensionmentioning

confidence: 99%

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Foucaud

Mertzios

Naserasr

et al. 2016

Graph-Theoretic Concepts in Computer Science

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Abstract. We study the problems Locating-Dominating Set and Metric Dimension, which consist of determining a minimum-size set of vertices that distinguishes the vertices of a graph using either neighbourhoods or distances. We consider these problems when restricted to interval graphs and permutation graphs. We prove that both decision problems are NP-complete, even for graphs that are at the same time interval graphs and permutation graphs and have diameter 2. While Locating-Dominating Set parameterized by solution size is trivially xed-parameter-tractable, it is known that Metric Dimension is W [2]-hard. We show that for interval graphs, this parameterization of Metric Dimension is xed-parameter-tractable.

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Section: Metric Dimensionmentioning

confidence: 99%

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Foucaud

Mertzios

Naserasr

et al. 2016

Graph-Theoretic Concepts in Computer Science

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“…Imran et al studied various degree based topological indices for various networks like silicates, hexagonal, honeycomb and oxide in [14]. For further study of topological indices of various graph families see, [2,9,10,12,13,15,18,[22][23][24][25]29,31,37]. …”

Section: Resultsmentioning

confidence: 99%

Computing topological indices of Sudoku graphs

Gao

Imran

Baig

et al. 2016

J. Appl. Math. Comput.

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In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (G A) index are used to predict the bioactivity of chemical compounds. A topological index is actually designed by transforming a chemical structure into a numeric number. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc. of chemical compounds. Graph theory has found a considerable use in this area of research. The topological indices of certain interconnection networks were studied recently by Imran et al. (Appl Math Comput 244:936-951, 2014). In this paper, we extend this study to n × n Sudoku graphs and derive analytical B Mohammad Reza Farahani

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“…There are many applications of resolving sets to problems of network discovery and verification [1], pattern recognition, image processing and robot navigation [2], geometrical routing protocols [10], connected joins in graphs [11] and coin weighing problems [12]. This problem has been studied for trees, multi-dimensional grids [2], Petersen graphs [13], torus networks [14], Benes networks [9], honeycomb networks [15], enhanced hypercubes [16] and Illiac networks [17].…”

Section: An Overview Of the Papermentioning

confidence: 99%

On Certain Connected Resolving Parameters of Hypercube Networks

Rajan¹,

William²,

Rajasingh³

et al. 2012

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Given a graph , a set is a resolving set if for each pair of distinct vertices there is a vertex such that . A resolving set containing a minimum number of vertices is called a minimum resolving set or a basis for . The cardinality of a minimum resolving set is called the resolving number or dimension of and is denoted by . A resolving set is said to be a star resolving set if it induces a star, and a path resolving set if it induces a path. The minimum cardinality of these sets, denoted respectively by

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On minimum metric dimension of honeycomb networks

Cited by 114 publications

References 9 publications

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Algorithms and Complexity for Metric Dimension and Location-domination on Interval and Permutation Graphs

Computing topological indices of Sudoku graphs

On Certain Connected Resolving Parameters of Hypercube Networks

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