Slot waveguides comprised of Ge23Sb7S70 and Si with and without graphene are considered for super-continuum generation in the mid-infrared range. The dispersion characteristics are optimized for the proposed waveguides comprised of Si and Ge23Sb7S70 chalcogenide as the core and cladding, respectively with and without graphene sheets embedded in the proposed structure. The proposed waveguide without graphene possesses all-normal dispersion and the super-continuum spectra with bandwidth of 1.75 µm is obtained for a pump with wavelength of 2 µm, peak power of 100 W, and time duration of 50 fs, at 20 dB level. Also, the total length of the waveguide is 8 mm. The optimized structure with three graphene sheets presents flat anomalous dispersion and the super-continuum spectra with bandwidth of 3 µm is obtained for a pump with wavelength, peak power, and time duration of 3 µm, 7 mW, and 50 fs, respectively at 10 dB level. It is demonstrated that the proper dispersion region for super-continuum generation depends on the sign of Kerr-index of the nonlinear material. The proposed waveguides are highly compatible with fabrication technologies for mid infrared applications.