  Background: Recently, transition quadrupole moments in rotational bands of
even-mass neutron-rich isotopes of molybdenum and ruthenium nuclei have been
measured. The new data have provided a challenge for theoretical descriptions
invoking stable triaxial deformations.
  Purpose: To understand experimental data on rotational bands in the
neutron-rich Mo-Ru region, we carried out theoretical analysis of moments of
inertia, shapes, and transition quadrupole moments of neutron-rich even-even
nuclei around $^{110}$Ru using self-consistent mean-field and shell model
techniques.
  Methods: To describe yrast structures in Mo and Ru isotopes, we use nuclear
Density Functional Theory (DFT) with the optimized energy density functional
UNEDF0. We also apply Triaxial Projected Shell Model (TPSM) to describe yrast
and positive-parity, near-yrast band structures.
  Results: Our self-consistent DFT calculations predict triaxial ground-state
deformations in $^{106,108}$Mo and $^{108.110,112}$Ru and reproduce the
observed low-frequency behavior of moments of inertia. As the rotational
frequency increases, a negative-$\gamma$ structure, associated with the aligned
$\nu(h_{11/2})^2$ pair, becomes energetically favored. The computed transition
quadrupole moments vary with angular momentum, which reflects deformation
changes with rotation; those variations are consistent with experiment. The
TPSM calculations explain the observed band structures assuming stable triaxial
shapes.
  Conclusions: The structure of neutron-rich even-even nuclei around $^{110}$Ru
is consistent with triaxial shape deformations. Our DFT and TPSM frameworks
provide a consistent and complementary description of experimental data.
