Fault-tolerant metric dimension of two-fold heptagonal-nonagonal circular ladder
Sunny Kumar Sharma, Vijay Kumar Bhat
Abstract
The problem of characterizing the classes of plane graphs with the bounded metric dimension, edge metric dimension, and fault-tolerant metric dimension is of great interest nowadays. In this paper, we study the metric dimension, the fault-tolerant metric dimension, and the edge metric dimension of a two-fold heptagonal-nonagonal circular ladder (denoted by [Formula: see text]). We show that the metric dimension and the edge metric dimension of [Formula: see text] are the same. We also study its fault-tolerant metric dimension and prove that the metric basis and the edge metric basis sets are independent.
Topics & Concepts
Metric dimensionMetric (unit)MathematicsDimension (graph theory)Bounded functionTopology (electrical circuits)Equivalence of metricsBasis (linear algebra)CombinatoricsInjective metric spaceMetric spaceDiscrete mathematicsGeometryMathematical analysisGraphEngineeringChordal graph1-planar graphOperations managementGraph Labeling and Dimension Problemsgraph theory and CDMA systemsGraph theory and applications