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In a graph G with a distribution of pebbles on its vertices, a pebbling move is the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. A weight function on G is a non-negative integer-valued…

Combinatorics · Mathematics 2007-05-23 Annalies Vuong , M. Ian Wyckoff

Given a configuration of pebbles on the vertices of a connected graph $G$, a \emph{pebbling move} removes two pebbles from some vertex and places one pebble on an adjacent vertex. The \emph{pebbling number} of a graph $G$ is the smallest…

Combinatorics · Mathematics 2017-06-14 Daniel W. Cranston , Luke Postle , Chenxiao Xue , Carl Yerger

Graph pebbling is a game played on a connected graph G. A player purchases pebbles at a dollar a piece, and hands them to an adversary who distributes them among the vertices of G (called a configuration) and chooses a target vertex r. The…

Combinatorics · Mathematics 2008-11-21 D. Curtis , T. Hines , G. Hurlbert , T. Moyer

A pebbling move refers to the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given an initial distribution of pebbles, use pebbling moves to reach a specified goal…

Combinatorics · Mathematics 2018-01-29 Garth Isaak , Matthew Prudente

Pebbling on graphs is a two-player game which involves repeatedly moving a pebble from one vertex to another by removing another pebble from the first vertex. The pebbling number $\pi(G)$ is the least number of pebbles required so that,…

Combinatorics · Mathematics 2018-01-25 John Asplund , Glenn Hurlbert , Franklin Kenter

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one…

Combinatorics · Mathematics 2015-03-18 Glenn Hurlbert

Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of two pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of…

Combinatorics · Mathematics 2012-11-20 Liliana Alcón , Marisa Gutierrez , Glenn Hurlbert

Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\vert f\vert=\sum_{u\in V}f(u)$ is called the weight of $f$ which is just the…

Combinatorics · Mathematics 2024-02-21 Fatemeh Aghaei , Saeid Alikhani

The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and…

Combinatorics · Mathematics 2014-02-07 Zheng-Jiang Xia , Yong-Liang Pan , Jun-Ming Xu

A pebbling move on a graph consists of taking two pebbles off from one vertex and add one pebble on an adjacent vertex, the $t$-pebbling number of a graph $G$ is the minimum number of pebbles so that we can move $t$ pebbles on any vertex on…

Combinatorics · Mathematics 2019-07-02 Zheng-Jiang Xia , Zhen-Mu Hong

Given a configuration of indistinguishable pebbles on the vertices of a graph, a pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling number of a graph is the least…

Combinatorics · Mathematics 2024-12-02 Jonad Pulaj , Kenan Wood , Carl Yerger

Graph pebbling is a game played on graphs with pebbles on their vertices. A pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. A configuration $C$ is a supply of pebbles at various vertices of a…

Combinatorics · Mathematics 2026-01-26 Matheus Adauto , Viktoriya Bardenova , Yunus Bidav , Glenn Hurlbert

Let $G=(V,E)$ be a simple graph. A function $\phi:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\sum_{u\in V}\phi(u)$ is called the size of $\phi$ which is just the total…

Combinatorics · Mathematics 2024-02-16 Saeid Alikhani , Fatemeh Aghaei

Consider a configuration of pebbles on the vertices of a connected graph. A pebbling move is to remove two pebbles from a vertex and to place one pebble at the neighbouring vertex of the vertex from which the pebbles are removed. For a…

Combinatorics · Mathematics 2025-04-01 I. Dhivviyanandam , A. Lourdusamy , S. Kither Iammal , K. Christy Rani

Suppose that pebbles are distributed on the vertices of a graph G. A pebbling step along an edge uv removes two pebbles from u and places one pebble on v. We introduce two new graph parameters: stack(G): the least integer t such that every…

Combinatorics · Mathematics 2026-04-27 Tamás Csernák , Lajos Soukup

The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and…

Combinatorics · Mathematics 2017-05-02 Zheng-Jiang Xia , Zhen-Mu Hong , Fu-Yuan Chen

For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a…

Combinatorics · Mathematics 2007-05-23 Jonas Sjostrand

Graph pebbling is a game played on graphs with pebbles on their vertices. A pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. The pebbling number $\pi(G)$ is the smallest $t$ so that from any…

Combinatorics · Mathematics 2024-03-05 Matheus Adauto , Celina de Figueiredo , Glenn Hurlbert , Diana Sasaki

Given a configuration of pebbles on the vertices of a graph $G$, a pebbling move removes two pebbles from a vertex and puts one pebble on an adjacent vertex. The pebbling number of a graph $G$ is the smallest number of pebbles required such…

Combinatorics · Mathematics 2024-11-26 Marshall Yang , Carl Yerger , Runtian Zhou

Consider a distribution of pebbles on a graph. A pebbling move removes two pebbles from a vertex and place one at an adjacent vertex. A vertex is reachable under a pebble distribution if it has a pebble after the application of a sequence…

Combinatorics · Mathematics 2023-01-25 László F. Papp