  We present our new model for the description of the very high energy Galactic
gamma-ray emission based on a discrete injection of cosmic rays by individual
sources. We investigate the morphology of the very high energy gamma-ray sky,
the detectability of cosmic-ray sources and the clumpiness of the diffuse
gamma-ray flux, assuming two different scenarios for cosmic-ray propagation.
Namely, a standard isotropic and homogeneous diffusion process and an isotropic
and inhomogeneous diffusion process. We notably formulate a possible
explanation to the small number of hadronic PeVatrons recently detected by
LHAASO. In the case of the inhomogeneous diffusion process, we constrain the
number of hadronic PeVatrons to be small. Finally, we give an argument that may
explain the discrepancy between the interstellar gas density distribution and
the very high energy diffuse gamma-ray flux.
