%0 Journal Article
%T Pebbling on $C_{4k+3}\times G$ and $M(C_{2n})\times G$
%A Zheng-Jiang Xia
%A Yong-Liang Pan
%A Jun-Ming Xu
%J Mathematics
%D 2014
%I arXiv
%X The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. It is conjectured that for all graphs $G$ and $H$, $f(G\times H)\leq f(G)f(H)$. If the graph $G$ satisfies the odd two-pebbling property, we will prove that $f(C_{4k+3}\times G)\leq f(C_{4k+3})f(G)$ and $f(M(C_{2n})\times G)\leq f(M(C_{2n}))f(G)$, where $C_{4k+3}$ is the odd cycle of order $4k+3$ and $M(C_{2n})$ is the middle graph of the even cycle $C_{2n}$.
%U http://arxiv.org/abs/1402.0764v2