Fault-tolerant metric dimension of two-fold heptagonal-nonagonal circular ladder
Sunny Kumar Sharma, Vijay Kumar Bhat · Discrete Mathematics Algorithms and Applications · 2021
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.