Graham's Pebbling Conjecture Holds for the Product of a Graph and a Sufficiently Large Complete Graph

Authors

Nopparat Pleanmani, Khon Kaen UniversityFollow

Abstract

For connected graphs G and H, Graham conjectured that π(G □ H) ≤ π(G) π(H) where π(G), π (H), and π(G □ H) are the pebbling numbers of G, H, and the Cartesian product G □ H, respectively. In this paper, we show that the inequality holds when H is a complete graph of sufficiently large order in terms of graph parameters of G.

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Recommended Citation

Pleanmani, Nopparat (2020) "Graham's Pebbling Conjecture Holds for the Product of a Graph and a Sufficiently Large Complete Graph," Theory and Applications of Graphs: Vol. 7: Iss. 1, Article 1.
DOI: 10.20429/tag.2020.070101
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol7/iss1/1