  In network theory, the domination parameter is vital in investigating several
structural features of the networks, including connectedness, their tendency to
form clusters, compactness, and symmetry. In this context, various domination
parameters have been created using several properties to determine where
machines should be placed to ensure that all the places are monitored. To
ensure efficient and effective operation, a piece of equipment must monitor
their network (power networks) to answer whenever there is a change in the
demand and availability conditions. Consequently, phasor measurement units
(PMUs) are utilised by numerous electrical companies to monitor their networks
perpetually. Overseeing an electrical system which consists of minimum PMUs is
the same as the vertex covering the problem of graph theory, in which a subset
D of a vertex set V is a power dominating set (PDS) if it monitors generators,
cables, and all other components, in the electrical system using a few
guidelines. Hypercube is one of the versatile, most popular, adaptable, and
convertible interconnection networks. Its appealing qualities led to the
development of other hypercube variants. A fractal cubic network is a new
variant of the hypercube that can be used as a best substitute in case faults
occur in the hypercube, which was wrongly defined in [Eng. Sci. Technol. 18(1)
(2015) 32-41]. Arulperumjothi et al. have recently corrected this definition
and redefined this variant with the exact definition in [Appl. Math. Comput.
452 (2023) 128037]. This article determines the PDS of the fractal cubic
network. Further, we investigate the resolving power dominating set (RPDS),
which contrasts starkly with hypercubes, where resolving power domination is
inherently challenging.
