  We investigate the roles of deformation on the giant monopole resonance
(GMR), particularly the mixing of the giant quadrupole resonance (GQR) and the
effects of the neutron excess in the well-deformed nuclei around $^{110}$Zr and
in the drip-line nuclei around $^{140}$Zr by means of the deformed
quasiparticle-random-phase-approximation employing the Skyrme and the local
pairing energy-density functionals. It is found that the isoscalar (IS) GMR has
a two-peak structure, the lower peak of which is associated with the mixing
between the ISGMR and the $K^{\pi}=0^{+}$ component of the ISGQR. The
transition strengths of the lower peak of the ISGMR grows as the neutron number
increases. In the drip-line nuclei, the neutron excitation is dominant over the
proton excitation. We find for an isovector (IV) excitation the GMR has a
four-peak structure due to the mixing of the IS and IV modes as well as the
mixing of the $K^{\pi}=0^{+}$ component of the IVGQR. Besides the GMR, we find
the threshold strength generated by neutrons only.
