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Robert A. Beeler, Teresa W. Haynes and Kyle Murphy

R eferences [1] R.A. Beeler, T.W. Haynes and K. Murphy, An introduction to t-restricted optimal rubbling , Congr. Numer., to appear. [2] C. Belford and N. Sieben, Rubbling and optimal rubbling of graphs , Discrete Math. 309 (2009) 3436–3446. doi:10.1016/j.disc.2008.09.035 [3] T.A. Clarke, R.A. Hochberg and G.H. Hurlbert, Pebbling in diameter two graphs and products of paths , J. Graph Theory 25 (1997) 119–128. doi:10.1002/(SICI)1097-0118(199706)25:2⟨119::AID-JGT3⟩3.0.CO;2-P [4] R. Feng and J.Y. Kim, Graham’s pebbling conjecture on

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Biswajit Deb and Kalpesh Kapoor

. Hammack, W. Imrich and S. Klaˇzar, Handbook of Product Graphs, Second Edition (CRC Press, New York, 2011). [5] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969). [6] W. Imrich and S. Klavˇzar, Product Graphs, Structure and Recognition (John Wiley & Sons Inc., New York, 2000). [7] W. Woolsey Johnson and W.E. Story, Notes on the ”15” puzzle, Amer. J. Math. 2 (1879) 397-404. doi:10.2307/2369492 [8] D. Kornhauser, G. Miller, and P. Spirakis, Coordinating pebble motion on graphs, the diameter of