On the number of $k$-dominating independent sets in planar graphs

A set $J_k$ of graph vertices is said to be $k$-dominating independent ($k \geq 1$) if its vertices are pairwise adjacent and every vertex not in $J_k$ is adjacent to at least $k$ vertices in $J_k.$ In the present paper, we obtain new upper bounds for the number of $k$-dominating independent sets for $k \geq 2$ in some planar graph classes. Illustr. 7, bibliogr. 15.