  Signal processing on graphs is a recent research domain that aims at
generalizing classical tools in signal processing, in order to analyze signals
evolving on complex domains. Such domains are represented by graphs, for which
one can compute a particular matrix, called the normalized Laplacian. It was
shown that the eigenvalues of this Laplacian correspond to the frequencies of
the Fourier domain in classical signal processing. Therefore, the frequency
domain is not the same for every support graph. A consequence of this is that
there is no non-trivial generalization of Heisenberg's uncertainty principle,
that states that a signal cannot be fully localized both in the time domain and
in the frequency domain. A way to generalize this principle, introduced by
Agaskar and Lu, consists in determining a curve that represents a lower bound
on the compromise between precision in the graph domain and precision in the
spectral domain. The aim of this paper is to propose a characterization of the
signals achieving this curve, for a larger class of graphs than the one studied
by Agaskar and Lu.
