Redefining fractal cubic networks and determining their metric dimension and fault-tolerant metric dimension

Abstract

In network theory, distance parameters are crucial in analyzing structural aspects of the networks under investigation, including their symmetry, connectedness, and tendency to form clusters. To this end, the metric dimension and the fault-tolerant metric dimension are important distance invariants of networks. In this article, we consider fractal cubic networks, a variant of hypercubes. We first correct their definition from the seminal paper [Engineering Science and Technology, an International Journal 18 (2015) 32–41]. After that, we determine their metric dimension and fault-tolerant metric dimension, which is in striking contrast to the situation with hypercubes, where these invariants are intrinsically difficult.