Abstract
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 t - pebbling number of G is the smallest number, ft(G) such that from any distribution of ft(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.
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