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Rajan, B., Rajasingh, I., Cynthia, J.A. and Manuel, P. (2003) On Minimum Metric Dimension. Proceedings of the Indonesia-Japan Conference on Combinatorial Geometry and Graph Theory, Bandung, September 2003, 13-16.

has been cited by the following article:

• TITLE: Fault-Tolerant Resolvability of Certain Crystal Structures

  AUTHORS: Sathish Krishnan, Bharati Rajan

  KEYWORDS: Resolving Set, Metric Dimension, Fault-Tolerant metric Dimension, Crystal Structures, Bismuth Tri-Iodide, Lead Chloride, Quartz

  JOURNAL NAME: Applied Mathematics, Vol.7 No.7, April 25, 2016

  ABSTRACT: An ordered set W of vertices of a graph G is called a resolving set, if all the vertices of G are uniquely determined by the vector of distances to the vertices in W. The metric dimension of G is the minimum cardinality of a resolving set of G. A resolving set W for G is fault-tolerant if W\{v} is also a resolving set, for each v in W, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set. In this paper we determine the metric dimension and fault-tolerant metric dimension problems for the graphs of certain crystal structures.