Another Look of Rings Domination in Ladder Graph

For a nontrivial connected graphGwith no isolated vertex, a nonempty subsetD⊆V(G) is a rings dominatingset if each vertexv∈V−Dis adjacent to at least two vertices inV−D. Thus, the dominating setDofV(G) is a rings dominating set if for allv∈V−D,|N(v)∩(V−D)|≥2. The cardinality of minimum ringsdominating set ofGis the rings domination number ofG, denoted byγriwhereas the cardinality of maximumrings dominating set is the upper rings domination number and is denoted byγ′ri. Here, we determine howthe rings dominating set is constructed in the ladder graph with the inclusion of generated conditions for thistype of domination and give new approach for its parameter.