  The phenomena of shape evolution and shape coexistence in even-even
$^{88-126}$Zr and $^{88-126}$Mo isotopes is studied by employing covariant
density functional theory (CDFT) with density-dependent point coupling
parameter sets DD-PCX and DD-PC1, and with separable pairing interaction. The
results for rms deviation in binding energies, two-neutron separation energy,
the differential variation of two-neutron separation energy, and rms charge
radii, as a function of neutron number, are presented and compared with
available experimental data. In addition to the oblate-prolate shape
coexistence in $^{96-110}$Zr isotopes, the correlation between shape transition
and discontinuity in the observables are also examined. A smooth trend of
charge radii in Mo isotopes is found to be due to the manifestation of
triaxiality softness. The observed oblate and prolate minima are related to the
low single-particle energy level density around the Fermi level of neutron and
proton respectively. The present calculations also predict a deformed bubble
structure in $^{100}$Zr isotope.
