  The present work is devoted to study the dynamical evolution of the galaxies
in scalar-GaussBonnet gravity in relationship with the MOND paradigm. This
study is useful for giving meaning to the presence of a new gravitational
constant. The stability of dark matter is strongly dependent on matter energy
density. We interested in calculating the maximum rotational velocity of
galaxies. We show that rotating galaxies can be described by a new parameter
which depends on both on the minimum value of scalar fields and the effective
mass of this field. According to the observation data, we have shown that this
parameter is a constant.
