2011/06/08 by Stephanie Jones, Joshua D. Laison, Jones, Stephanie +6
Computer Science · Mathematics · #05C22 #05C57 #Artificial Intelligence in Games #Chaos-based Image/Signal Encryption #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05C22 #msc:05C57
paper · pdf · doi:10.48550/arxiv.1106.1625
18 pages, 7 figures
arxiv created 2011/06/08 · openalex publication_date 2011/06/08 · arxiv updated 2011/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We expand the theory of pebbling to graphs with weighted edges. In a weighted pebbling game, one player distributes a set amount of weight on the edges of a graph and his opponent chooses a target vertex and places a configuration of pebbles on the vertices. Player one wins if, through a series of pebbling moves, he can move at least one pebble to the target. A pebbling move of p pebbles across an edge with weight w leaves the floor of pw pebbles on the next vertex. We find the weighted pebbling numbers of stars, graphs with at least 2|V|-1 edges, and trees with given targets. We give an explicit formula for the minimum total weight required on the edges of a length-2 path, solvable with p pebbles and exhibit a graph which requires an edge with weight 1/3 in order to achieve its weighted pebbling number.