Optimal t-pebbling on paths and cycles

doi:10.3969/j.issn.0253-2778.2015.03.002

Journal of University of Science and Technology of China ›› 2015, Vol. 45 ›› Issue (3): 186-192.DOI: 10.3969/j.issn.0253-2778.2015.03.002

• Original Paper • Previous Articles

Optimal t-pebbling on paths and cycles

XIA Zhengjiang, PAN Yongliang, XU Junming

School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

Received:2014-11-14 Revised:2015-03-10 Accepted:2015-03-10 Online:2015-03-10 Published:2015-03-10
Contact: PAN Yongliang
About author:XIA Zhengjiang, male, born in 1987, PhD candidate. Research field: combinatorics and graph theory.
Supported by:
Supported by the Fundamental Research Funds for the Central Universities and the NNSF of China (61272008,11271348,10871189).

Abstract

Abstract: A pebbling move removes two pebbles from a vertex and places one pebble on one of its neighbours. For t≥1, the optimal t-pebbling number of a graph G, f′t(G), is the minimum number of pebbles necessary so that from some initial distribution of them it is possible to move t pebbles to any target vertex by a sequence of pebbling moves. f′(G)=f′1(G) be the optimal pebbling number of G. Here the optimal t-pebbling numbers of the path Pn and the cycle C5 were given, respectively. In the final section, it was obtained that f′9t(P2×P3)=20t, f′9t+1(P2×P3)=20t+3, and 20t+2r+1≤f′9t+r(P2×P3)≤20t+2r+2, for 2≤r≤8, the last equality holds for r=5,6,7,8.

Key words: optimal t-pebbling number, path, cycle, Cartesian product

CLC Number:

O157.

XIA Zhengjiang, PAN Yongliang, XU Junming. Optimal t-pebbling on paths and cycles[J]. Journal of University of Science and Technology of China, 2015, 45(3): 186-192.

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Optimal t-pebbling on paths and cycles

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