On 2-dominating kernels in graphs

A subset S ⊆ V (G) is an independent set of G if no two vertices of S are adjacent in G. A subset Q ⊆ V (G) is a 2-dominating set of G if each vertex from V (G)\Q has at least two neighbours in Q. We define new kind of kernels in graphs. Using existing concepts of an independent set and a 2-dominating set, we define in the natural way the concept of 2-dominating kernels in graphs. A subset J ⊂ V (G) is a 2-dominating kernel of G if J is independent and 2dominating. Clearly a 2-dominating kernel of G is a kernel of G. Every graph does not always posses a 2-dominating kernel. In the talk we give characterizations of some classes of graphs with 2-dominating kernels.