On spectrally optimal duals of frames generated by graphs

Recently, the concept of frames generated by graphs has been introduced in \cite{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.