On spectrally optimal duals of frames generated by graphs

Recently, the concept of frames generated by graphs has been introduced in D. In this paper, we study spectrally optimal dual frames of frames generated by graphs. We show that if the frame is generated by a connected graph, then its canonical dual frame is the unique spectrally optimal dual frame for 1-erasure and 2-erasures. Further, we show that the canonical dual frames of frames generated by disconnected graphs are non-unique spectrally optimal dual frames for 1-erasure and 2-erasures.