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Lollipop and cubic weight functions for graph pebbling

Author

Listed:
  • Marshall Yang
  • Carl Yerger

    (Davidson College)

  • Runtian Zhou

    (Duke University)

Abstract

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 that, given an arbitrary initial configuration of pebbles, one pebble can be moved to any vertex of G through some sequence of pebbling moves. Through constructing a non-tree weight function for $$Q_4$$ Q 4 , we improve the weight function technique, introduced by Hurlbert and extended by Cranston et al., that gives an upper bound for the pebbling number of graphs. Then, we propose a conjecture on weight functions for the n-dimensional cube. We also construct a set of valid weight functions for variations of lollipop graphs, extending previously known constructions.

Suggested Citation

  • Marshall Yang & Carl Yerger & Runtian Zhou, 2025. "Lollipop and cubic weight functions for graph pebbling," Journal of Combinatorial Optimization, Springer, vol. 49(1), pages 1-17, January.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:1:d:10.1007_s10878-024-01248-1
    DOI: 10.1007/s10878-024-01248-1
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