NDC Pebbling Number for Some Class of Graphs

Let G be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and the placing one pebble to an adjacent vertex and throwing away the another pebble. A dominating set D of a graph G = (V, E) is a non-split dominating set if the induced graph < V − D > is connected. The Non-split Domination Cover(NDC) pebbling number, ψns(G), of a graph G is the minimum of pebbles that must be placed on V(G) such that after a sequence of pebbling moves, the set of vertices with a pebble forms a non-split dominating set of G, regardless of the initial configuration of pebbles. We discuss some basic results and determine ψns for some families of standard graphs. © 2024 the Author(s), licensee Combinatorial Press.