Lollipop and cubic weight functions for graph pebbling

Marshall Yang, Carl Yerger () and Runtian Zhou ()
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Carl Yerger: Davidson College
Runtian Zhou: Duke University

Journal of Combinatorial Optimization, 2025, vol. 49, issue 1, No 16, 17 pages

Abstract: 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.

Keywords: Pebbling; Cube; Lollipop graph; Weight function; 05C22; 05C35; 05C57 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-024-01248-1

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