Abstract
In this paper we introduce a new order on the set of n- dimensional tuples and prove that this order preserves nestedness in the edge isoperimetric problem for the graph P n, defined as the n th cartesian power of the well-known Petersen graph. Thus, we show, that there is a graph for which powers the solution of the edge isoperimetric problem preserve nestedness and it is different from the lexicographic order. With respect to this result we determine the cutwidth and wirelength of P n. These results are then generalized to the cartesian product of P n and the m-dimensional binary hypercube.
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