• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.163-176
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• 2019

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, $f_t(G)$, of a connected graph G, is the smallest positive integer such that from every placement of $f_t(G)$ pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than $2f_t(G)$ - q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree $M(B_h)$ and we show that the middle graph of a complete binary tree $M(B_h)$ satisfies the 2t-pebbling property.

• 자연과학논문집
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• 제12권1호
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• pp.1-9
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• 2002

연결 그래프의 꼭지점에 자갈이 분포되어 있다고 하자. 한 꼭지점에서 두 개의 자갈을 취하여 한 개의 자갈만을 인접한 꼭지점에 보내는 이동을 할 때, 자갈이 분포될 수 있는 모든 경우에서 임의의 꼭지점에 한 개의 자갈을 보내기 위해 필요한 최소의 자갈의 수를 그 그래프의 pebbling number 라고 한다. 이 논문에서 Petersen Graph의 pebbling 수를 계산하였고 complete bipartite 그래프 $K_{m,n}$과 꼭지점의 수 h가 4개 이상인 complete 그래프의 categorical product 의 pebbling number가 (m+n)h 이 됨을 보였다.

• 충청수학회지
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• 제14권1호
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• pp.7-14
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• 2001

Let G be a connected graph. A pebbling move on a graph G is taking two pebbles off one vertex and placing one of them on an adjacent vertex. The pebbling number of a connected graph G, f(G), is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the lexicographic products of some graphs are computed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.57-61
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• 2002

Let G be a connected graph. A pebbling move on a graph G is the movement of taking two pebbles off from a vertex and placing one of them onto an adjacent vertex. The pebbling number f(G) of a connected graph G is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the compositions of two graphs are computed.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.77-83
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• 2024

Chung defined a pebbling move on a graph G as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The monophonic pebbling number guarantees that a pebble can be shifted in the chordless and the longest path possible if there are any hurdles in the process of the supply chain. For a connected graph G a monophonic path between any two vertices x and y contains no chords. The monophonic pebbling number, µ(G), is the least positive integer n such that for any distribution of µ(G) pebbles it is possible to move on G allowing one pebble to be carried to any specified but arbitrary vertex using monophonic a path by a sequence of pebbling operations. The aim of this study is to find out the monophonic pebbling numbers of the sun graphs, (C_n × P₂) + K₁ graph, the spherical graph, the anti-prism graphs, and an n-crossed prism graph.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.121-134
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• 2008

A pebbling step on a graph consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The covering cover pebbling number of a graph is the smallest number of pebbles, such that, however the pebbles are initially placed on the vertices of the graph, after a sequence of pebbling moves, the set of vertices with pebbles forms a covering of G. In this paper we find the covering cover pebbling number of n-cube and diameter two graphs. Finally we give an upperbound for the covering cover pebbling number of graphs of diameter d.

• 호남수학학술지
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• 제32권4호
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• pp.769-776
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• 2010

A pebbling move on a connected graph G is taking two pebbles off of one vertex and placing one of them on an adjacent vertex. For a connected graph G, $G^p$ (p > 1) is the graph obtained from G by adding the edges (u, v) to G whenever 2 $\leq$ dist(u, v) $\leq$ p in G. And the pebbling exponent of a graph G to be the least power of p such that the pebbling number of $G^p$ is equal to the number of vertices of G. We compute the pebbling number of fourth power of paths so that the pebbling exponents of some paths are calculated.

• 충청수학회지
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• 제19권4호
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• pp.403-408
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• 2006

A pebbling move on a connected graph G is taking two pebbles off of one vertex and placing one of them on an adjacent vertex. The domination cover pebbling number ${\psi}(G)$ is the minimum number of pebbles required so that any initial configuration of pebbles can be transformed by a sequence of pebbling moves so that the set of vertices that contain pebbles forms a domination set of G. We determine the domination cover pebbling number for fans, fuses, and pseudo-star.