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Fault-Tolerant Resolvability of Certain Crystal Structures
Research and Development Centre, Bharathiar University, Coimbatore, India
Department of Mathematics, Loyola College, Chennai, India
Department of Mathematics, DMI College of Engineering, Chennai, India
School of Mathematical and Physical Sciences, Faculty of Science and IT, The University of Newcastle, Callaghan, Australia
- 1 Research and Development Centre, Bharathiar University, Coimbatore, India
- 2 Department of Mathematics, Loyola College, Chennai, India
- 3 Department of Mathematics, DMI College of Engineering, Chennai, India
- 4 School of Mathematical and Physical Sciences, Faculty of Science and IT, The University of Newcastle, Callaghan, Australia
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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.
KeywordsResolving SetMetric DimensionFault-Tolerant metric DimensionCrystal StructuresBismuth Tri-IodideLead ChlorideQuartz
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