In order to investigate the correlation between the circular velocity V _ { c } and the central velocity dispersion of the spheroidal component \sigma _ { c } , we analyzed these quantities for a sample of 40 high surface brightness disc galaxies ( hereafter HSB ) , 8 giant low surface brightness spiral galaxies ( hereafter LSB ) , and 24 elliptical galaxies characterized by flat rotation curves .
Galaxies have been selected to have a velocity gradient \leq 2 km s ^ { -1 } kpc ^ { -1 } for R \geq 0.35 R _ { 25 } .
We used these data to better define the previous V _ { c } – \sigma _ { c } correlation for spiral galaxies ( which turned out to be HSB ) and elliptical galaxies , especially at the lower end of the \sigma _ { c } values .
We find that the V _ { c } – \sigma _ { c } relation is described by a linear law out to velocity dispersions as low as \sigma _ { c } \approx 50 km s ^ { -1 } , while in previous works a power law was adopted for galaxies with \sigma _ { c } > 80 km s ^ { -1 } .

Elliptical galaxies with V _ { c } based on dynamical models or directly derived from the H I rotation curves follow the same relation as the HSB galaxies in the V _ { c } – \sigma _ { c } plane .
On the contrary , the LSB galaxies follow a different relation , since most of them show either higher V _ { c } ( or lower \sigma _ { c } ) with respect to the HSB galaxies .
This argues against the relevance of baryon collapse in the radial density profile of the dark matter haloes of LSB galaxies .
Moreover , if the V _ { c } – \sigma _ { c } relation is equivalent to one between the mass of the dark matter halo and that of the supermassive black hole , these results suggest that the LSB galaxies host a supermassive black hole with a smaller mass compared to HSB galaxies of equal dark matter halo .
On the other hand , if the fundamental correlation of SMBH mass is with the halo circular velocity , then LSBs should have larger black hole masses for given bulge dispersion .

Elliptical galaxies with V _ { c } derived from H I data and LSB galaxies were not considered in previous studies .