Optimal Cuts for Powers of the Petersen Graph (original) (raw)

Lecture Notes in Computer Science, 1999

Abstract

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 , dened 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 dierent 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. 1 Introduction The subject of the paper is the edge-isoperimetric problem, which consists of nding a subset of vertices of a given graph, such that the number of edges separating this subset from its complement, also called edge cut, has minimal size among all subsets of the same cardinality. For a graph G = (VG ; EG ) with vertex set VG , edge set EG and A VG denote G (A) = f(u...

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