Another example is the perfect dominating set problem also known as efficient dominating set or 1-perfect code in graphs. The problem is to decide the existence of a dominating set $C$ such that the shortest path between any two nodes in the dominating set $C$ is at least 3 (edges). The problem was proven to be $NP$-complete independently by many researchers. The problem remains $NP$-complete even for cubic planar graphs.

Another example is the efficient dominating set problem also known as 1-perfect code in graphs. The problem is to determine the existence of a dominating set $C$ in undirected graph such that the shortest path between any two nodes in the dominating set $C$ is at least 3 (edges). The problem was proven to be $NP$-complete independently by many researchers. The problem remains $NP$-complete even for cubic planar graphs.

D. W. Bange, A. E. Barkauskas, and P. J. Slater. Efficient dominating sets in graphs. Applications of discrete mathematics, Proc. 3rd SIAM Conf., Clemson/South Carolina 1986, 189-199 (1988)., 1988.