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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.

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