  We have investigated the Kondo physics of a single magnetic impurity embedded
in multi-Dirac (Weyl) node fermionic systems. By using a generic effective
model for the host material and employing a numerical renormalization group
approach we access the low temperature behavior of the system, identifying the
existence of Kondo screening in single-, double-, and triple-Dirac (Weyl) node
models. We find that in any multi-Dirac node systems the low-energy regime lies
within one of the known classes of pseudogap Kondo problem, extensively studied
in the literature. Kondo screening is also observed for time reversal symmetry
broken Weyl systems. This is, however, possible only in the particle-hole
symmetry broken regime obtained for finite chemical potential $\mu$. Although
weakly, breaking time-reversal symmetry suppresses the Kondo resonance,
especially in the single-node Weyl semimetals. More interesting Kondo screening
regimes are obtained for inversion symmetry broken multi-Weyl fermions. In
these systems the Kondo regimes of double- and triple-Weyl node models are much
richer than in the single-Weyl node model. While in the single-Weyl node model
the Kondo temperature increases monotonically with $|\mu|$ regardless the value
of the inversion symmetry breaking parameter $Q_0$, in double- and triple-Weyl
node models there are two distinct regimes: (i) For $Q_0< |\mu|$ the Kondo
temperature depends strongly on $\mu$, while (ii) for $Q_0 > |\mu|$ the Kondo
temperature depends very weakly on $\mu$, resembling the flat-band single
impurity Anderson model.
