  In an analytical way of studying matter effects on neutrino oscillations, the
Naumov and Toshev relations have been derived to respectively link the Jarlskog
invariant of CP violation and the Dirac phase in the standard parametrization
of the $3\times 3$ flavor mixing matrix to their matter-corrected counterparts.
Here we show that there exist similar relations for Dirac neutrinos and charged
leptons evolving with energy scales via the one-loop renormalization-group (RG)
equations in the tau-dominance approximation, and for the running behaviors of
up- and down-type quarks in the top-dominance approximation, provided a
different parametrization is taken into account.
