title: The fault-tolerant metric dimension of the king’s graph
metadata.name: dc.contributor.author
metadata.value: Voronov, Roman V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-10-12T09:34:49Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-10-12T09:34:49Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Voronov R. V. The fault-tolerant metric dimension of the king’s graph. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 3, pp. 241–249.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8510
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The concept of resolving the set within a graph is related to the optimal placement problem of
  access points in an indoor positioning system. A vertex w of the undirected connected graph
  G resolves the vertices u and v of G if the distance between vertices w and u differs from the
  distance between vertices w and v. A subset W of vertices of G is called a resolving set, if every
  two distinct vertices of G are resolved by some vertex of w ∈ W. The metric dimension of G
  is a minimum cardinality of its resolving set.The set of access points of the indoor positioning
  system corresponds to the resolving set of vertices in the graph.The minimum number of access
  points required to locate each of the vertices corresponds to the metric dimension of graph. A
  resolving set W of the graph G is fault-tolerant if Wminus{w} is also a resolving set of G,
  for each w ∈ W. The fault-tolerant metric dimension of the graph G is a minimum cardinality
  of the fault-tolerant resolving set. In the indoor positioning system the fault-tolerant resolving
  set provides correct information even when one of the access points is not working. The article
  describes a special case of a graph called the king’s graph, or the strong product of two paths.The
  king’s graph is a building model in some indoor positioning systems. In this article we give an
  upper bound for the fault-tolerant metric of the king’s graph and a formula for a particular
  case of the king’s graph. Refs 20. Figs 2.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: fault-tolerant metric dimension
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strong product graphs
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: king’s graph
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: access points of indoor positioning system
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The fault-tolerant metric dimension of the king’s graph
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 02-Voronov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8510/1/02-Voronov.pdf
resources.format: Adobe PDF
resources.size: 238,94 kB