DETOUR PEBBLING ON CARTESIAN PRODUCT GRAPHS

Given a distribution of pebbles on the vertices of a connected graph $G$, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles on an adjacent vertex. The {\it $t$ - pebbling number} of $G$ is the smallest number, $f_t(G)$ such that from any distribution of $f_t(G)$ pebbles, it is possible to move $t$ pebbles to any specified target vertex by a sequence of pebbling moves. The detour pebbling number of a graph $f^*(G)$ is the smallest number such that from any distribution of $f^*(G)$ pebbles, it is possible to move a pebbles to any specified target vertex by a sequence of pebbling moves using a detour path. In this paper, we find the detour pebbling number for some Cartesian product graphs and also the detour $t$ - pebbling number for those cartesian product graphs.