For connected graphs $G$ and $H$, Graham conjectured that $\pi(G\square H)\leq\pi(G)\pi(H)$ where $\pi(G), \pi(H)$, and $\pi(G\square H)$ are the pebbling numbers of $G$, $H$, and the Cartesian product $G\square H$, 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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"Graham's Pebbling Conjecture Holds for the Product of a Graph and a Sufficiently Large Complete Graph,"
Theory and Applications of Graphs: Vol. 7
, Article 1.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol7/iss1/1