Physical Sciences and Mathematics Commons^™

Graham's Pebbling Conjecture Holds For The Product Of A Graph And A Sufficiently Large Complete Graph, Nopparat Pleanmani

Theory and Applications of Graphs

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.