Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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PEBBLING EXPONENTS OF PATHS

  • Kim, Ju-Young (Department of Mathematics, Catholic University of Daefu) ;
  • Kim, Sun-Ah (Department of Mathematics, Chosun University)
  • Received : 2010.11.19
  • Accepted : 2010.12.11
  • Published : 2010.12.25
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Abstract

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.

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References

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