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An extension (K(X)|K, v) of valued fields is said to be valuationtranscendental if we have equality in the Abhyankar inequality. Minimal pairsof definition are fundamental objects in the investigation of valuationtranscendental extensions. In this article, we associate a uniquely determinedpositive integer with a valuation transcendental extension. This integer isdefined via a chosen minimal pair of definition, but it is later shown to beindependent of the choice. Further, we show that this integer encodes importantinformation regarding the implicit constant field of the extension (K(X)|K, v).

Minimal pairs, inertia degrees, ramification degrees and implicit constant fields