  We give a notion of quantum automorphism group of graph C*-algebras without
sink at critical inverse temperature. This is defined to be the universal
object of a category of CQG's having a linear action in the sense of [11] and
preserving the KMS state at critical inverse temperature. We show that this
category for a certain KMS state at critical inverse temperature coincides with
the category introduced in [11] for a class of graphs. We also introduce an
orthogonal filtration on Cuntz algebra with respect to the unique KMS state and
show that the category of CQG's preserving the orthogonal filtration coincides
with the category introduced in this paper.
