An Edge-Isoperimetric Problem for Powers of the Petersen Graph

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 Pⁿ, defined as the nth cartesian power of the well-known Petersen graph. The cutwidth and wirelength of Pⁿ are also derived. These results are then generalized for the cartesian product of Pⁿ and the m-dimensional binary hypercube.