Author(s)

Sathish Krishnan^1,2, Bharati Rajan^3,4

¹Research and Development Centre, Bharathiar University, Coimbatore, India.
²Department of Mathematics, DMI College of Engineering, Chennai, India.
³Department of Mathematics, Loyola College, Chennai, India.
⁴School of Mathematical and Physical Sciences, Faculty of Science and IT, The University of Newcastle, Callaghan, Australia.

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.

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

Krishnan, S. and Rajan, B. (2016) Fault-Tolerant Resolvability of Certain Crystal Structures. Applied Mathematics, 7, 599-604. doi: 10.4236/am.2016.77055.