Optimal Cuts for Powers of the Petersen Graph

Authors:
Sergej L. Bezrukov;Sajal K. Das;Robert Elsässer
Affiliations:
-;-;-
Venue:
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Year:
1999

Citing 5
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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 Pn, defined as the nth 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 Pn. These results are then generalized to the cartesian product of Pn and the m-dimensional binary hypercube.