undefined

undefined

doi:undefined

https://doi.org/10.2478/jamsi-2025-0002

2-target pebbling number of graphs

May 1, 2025
Journal of Applied Mathematics, Statistics and Informatics
A Lourdusamy +2 more

Listen

Abstract

Translate Article

Take Notes

Abstract Chung defined the pebbling move of a graph which involves choosing a vertex with at least two pebbles, discarding those two pebbles from that vertex and adding one pebble to a nearby vertex. The 2-target pebbling number of the vertices u,v in graph a G is the least number φ(G,u,v) has the characteristic that for every configuration of φ(G,u,v) pebbles on G, it is possible to move a pebble to u and v simultaneously by a sequence of pebbling moves. The 2-target pebbling number of graph G, denoted by φ(G), is the maximum φ(G,u,v) over all pairs of the vertices in G. In this paper, we discuss the 2-target pebbling number for some standard graphs.

Similar Papers

Research Article
10.61091/jcmcc119-13

NDC Pebbling Number for Some Class of Graphs

Mar 31, 2024
Journal of Combinatorial Mathematics and Combinatorial Computing
A Lourdusamy + 2 more

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  is connected. The Non-split Domination Cover(NDC) pebbling number, $\psi_{ns}(G)$, 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 and determine $\psi_{ns}$ for some families of standard graphs.