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In structural pattern recognition, given a set of graphs, the computation ofa Generalized Median Graph is a well known problem. Some methods approach theproblem by assuming a relation between the Generalized Median Graph and theCommon Labelling problem. However, this relation has still not been formallyproved. In this paper, we analyse such relation between both problems. The mainresult proves that the cost of the common labelling upper-bounds the cost ofthe median with respect to the given set. In addition, we show that the twoproblems are equivalent in some cases.

On the Relation Between the Common Labelling and the Median Graph