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.