Non-split Domination Cover Pebbling Number for Some Class of Middle Graphs

2023/05/08 by A. Lourdusamy, Lourdusamy, A., I. Dhivviyanandam +3
Computer Science · #05C12 #05C25 #05C38 #05C76 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.04463

openalex publication_date 2023/05/08 · openalex created_date 2023/05/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and placing one pebble to an adjacent vertex and throwing away the other pebble. The non-split domination cover pebbling number, ψ_ns(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, NP-completeness of non-split domination number, and determine ψ_ns for some families of Middle graphs.

Related

• Domination Cover Pebbling: Graph Families
• Cover pebbling numbers and bounds for certain families of graphs
• The Cover Pebbling Number of Graphs
• The cover pebbling theorem
• Pebbling in Split Graphs