Abstract
The profile minimization problem arose from the study of sparse matrix technique. In terms of graphs, the problem is to determine the profile of a graph G which is defined as P ( G ) = min f ∑ v ∈ V ( G ) max x ∈ N [ v ] ( f ( v ) - f ( x ) ) , where f runs over all bijections from V ( G ) to { 1 , 2 , … , | V ( G ) | } and N [ v ] = { v } ∪ { x ∈ V ( G ) : xv ∈ E ( G ) } . The main result of this paper is to determine the profiles of K m × K n , K s , t × K n and P m × K n .
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