Pebbling numbers of some graphs

作     者：冯荣权 Ju Young Kim 

作者机构：School of Mathematical Sciences Peking University Beijing 100871 China Department of Mathematics Catholic University of Daegu Kyongsan 713-702 Korea 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2002年第45卷第4期

页      面：470-478页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No. 10001005) and by RFDP of China 

主　　题：pebbling, Graham's conjecture, Cartesian product, fan graph, wheel graph. 

摘      要：Chung defined a pebbling move on a graphG as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number of a connected graphG, f(G), is the leastn such that any distribution ofn pebbles onG allows one pebble to be moved to any specified but arbitrary vertex by a sequence of pebbling moves. Graham conjectured that for any connected graphsG andH, f(G xH) ≤ f(G)f(H). In the present paper the pebbling numbers of the product of two fan graphs and the product of two wheel graphs are computed. As a corollary, Graham’s conjecture holds whenG andH are fan graphs or wheel graphs.