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Let  G  be a finite  π -separable group, where  π  is a set of primes, and let  χ  be an irreducible complex character that is a  π -lift of some  π -partial character of  G . It was proved by Cossey and Lewis that all of the vertex pairs for  χ  are linear and conjugate in  G  if, but the result can fail for. In this paper we introduce the notion of the linear twisted vertices in the case where, and then establish the uniqueness for such vertices under the conditions that either  χ  is an-lift for a  π -chainof  G  or it has a linear Navarro vertex, thus answering a question proposed by them.

The uniqueness of vertex pairs in π -separable groups