  With the wide application of spectral and algebraic theory in discrete signal
processing techniques in the field of graph signal processing, an increasing
number of signal processing methods have been proposed, such as the graph
Fourier transform, graph wavelet transform and windowed graph Fourier
transform. In this paper, we propose and design the definition of the discrete
linear canonical transform on graphs (GLCT), which is an extension of the
discrete linear canonical transform (DLCT), just as the graph Fourier transform
(GFT) is an extension of the discrete Fourier transform (DFT). First, based on
the centrality and scalability of the DLCT eigendecomposition approach, the
definition of GLCT is proposed by combining graph chirp-Fourier transform,
graph scale transform and graph fractional Fourier transform. Second, we derive
and discuss the properties and special cases of GLCT. Finally, some GLCT
examples of the graph signals are given to illustrate the improvement of the
transformation.
