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A pebbling move on a graph $G$ consists of taking two pebbles off one vertexand placing one on an adjacent vertex. The pebbling number of a graph $G$,denoted by $f(G)$, is the least integer $n$ such that, however $n$ pebbles arelocated on the vertices of $G$, we can move one pebble to any vertex by asequence of pebbling moves. Let $M(G)$ be the middle graph of $G$. For anyconnected graphs $G$ and $H$, Graham conjectured that $f(G\times H)\leqf(G)f(H)$. In this paper, we give the pebbling number of some graphs and provethat Graham's conjecture holds for the middle graphs of some even cycles.

Graham's pebbling conjecture on Cartesian product of the middle graphs of even cycles