Resolvability in graphs and the metric dimension of a graph

By G. Chartrand, Linda Eroh, Mark A. Johnson, O. Oellermann. Discrete Applied Mathematics, 2000

971 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8a7d4d1b4ddc4322b2824e901282296df6bd59d7

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In Computational Theory and Mathematics

Citations in the corpus

On the Local Metric Dimension of Corona Product Graphs (2013, result): “This invariant was studied further in a number of other papers including, for instance [1, 4, 5, 7, 8, 10, 14, 16, 19].”
On the Metric Dimension of Cartesian Products of Graphs (2005, background): “Slater [42], and subsequently a number of other authors [9, 24, 27], proved that for every tree T that is not a path,”
The k-metric dimension of a graph (2013, background): “This invariant was studied further in a number of other papers including for example, [3, 4, 5, 7, 8, 10, 16, 17, 21, 22, 23].”
The local metric dimension of a graph (2010, background): “In recent years, this concept has been studied widely (see [4], [5], [13], [15], [17], [19], [20], [21], for example) with a variety of applications.”
Base size, metric dimension and other invariants of groups and graphs (2011, background): “In graph theory, it is a parameter that has appeared in various applications, as diverse as combinatorial optimization [85], pharmaceutical chemistry [39], robot navigation [71] and sonar [90], to name but a few.”
Fault-Tolerant Resolvability and Extremal Structures of Graphs (2019, background): “The vertex–edge relation in graphs and its equivalence to the atom–bond relation derive many applications in chemistry [6].”
Metric-based resolvability of polycyclic aromatic hydrocarbons (2021, background): “Metric dimension is extensively applied in the various fields of science such as facility location problems, sonar and coastguard Loran [42], computer networks [28], combinatorial optimization [39], robot navigation [23], pharmaceutical chemistry [6], weighing problems [43], and image processing, fo”
On the Commuting Graph of Dihedral Group (2016, methodology): “It is a parameter that has appeared in various applications of graph theory, as diverse as pharmaceutical chemistry [5, 7], robot navigation [14], combinatorial optimization [16], and sonar and Coast Guard LORAN [17], to name a few.”