  The notions of dominating sets of graphs began almost 400 years ago with the
game of chess, which sparked the analysis of dominating sets of graphs, at
first relatively loosely until the beginnings of the 1960s, when the issue was
given mathematical description. It's among the most important problems in graph
theory, as well as an NP-Complete problem that can't be solved in polynomial
time. As a result, we describe a new hybrid cuckoo search technique to tackle
the MDS problem in this work. Cuckoo search is a well-known metaheuristic famed
for its capacity for exploring a large area of the search space, making it
useful for diversification. However, to enhance performance, we incorporated
intensification techniques in addition to the genetic crossover operator in the
suggested approach. The comparison of our method with the corresponding
state-of-the-art techniques from the literature is presented in an exhaustive
experimental test. The suggested algorithm outperforms the present state of the
art, according to the obtained results.
