  We report the temperature and magnetic field dependence of resistivity
($\rho$) for single-crystalline EuTi$_{1-x}$Nb$_{x}$O$_3$ ($x$=0.10$-$0.20), an
itinerant ferromagnetic system with very low Curie temperature ($T_C$). The
detailed analysis reveals that the charge conduction in
EuTi$_{1-x}$Nb$_{x}$O$_3$ is extremely sensitive to Nb concentration and
dominated by several scattering mechanisms. Well below the $T_C$, where the
spontaneous magnetization follows the Bloch's $T^{3/2}$ law, $\rho$ exhibits
$T^2$ dependence with a large coefficient $\sim$10$^{-8}$ $\Omega$ cm K$^{-2}$
due to the electron-magnon scattering. Remarkably, all the studied samples
exhibit a unique resistivity minimum at $T$$=$$T_{\rm min}$ below which $\rho$
shows logarithmic increment with $T$ (for $T_{\rm C}$$<$$T$$<$$T_{\rm min}$)
due to the Kondo scattering of Nb 4$d^1$ itinerant electrons by the localized
4$f$ moments of Eu$^{2+}$ ions which suppresses strongly with applied magnetic
field. In the paramagnetic state, $T^{2}$ and $T^{3/2}$ dependence of the
resistivity have been observed, suggesting an unusual crossover from a
Fermi-liquid to a non-Fermi-liquid behavior with increasing $T$. The observed
temperature and magnetic field dependence of resistivity has been analysed
using different theoretical models.
