This is where the answer changes from "have you tried google", to "it depends".

There are two main contributions to dispersion in single mode fibres. 

• Material dispersion - which depends on the composition of core and gladding glasses.
• Waveguide dispersion - which depends on the shape of the refractive index profile and on the relative index difference, Δ.

In a real optical fibre these contributions interact, and other factors such as the wavelength dependence of the relative index difference Δ must be included.

In a step index fibre (as specified in your previous question), and in the absence of material dispersion, waveguide dispersion is a minimum for normalised frequency V0 approximately 3 - just beyond the theoretical frequency for single mode operation (VC = 2.4048).  Group velocity is a minimum at V~3, so pulse delay decreases with increasing frequency further into the multimode region (anomalous dispersion), and delay increases with increasing frequency (normal dispersion) in the single mode region.

In the absence of material dispersion, if you increase Δ, and keep everything else constant, the cut-off wavelength will shift to longer wavelengths, and so will the dispersion zero wavelength:  λ0  = π d sqrt( 2 n1Δ )  /  V0  where V0 ~ 3.

If material dispersion is present, then the result depends on both normalised frequency (V = π d sqrt( 2 n1Δ ) / λ) and on Δ. 

The magnitude of waveguide component of dispersion is proportional to the the product D V Δ, where D is a dimensionless function of V, and is only weakly dependent on Δ (independent of Δ in the weak guidance limit where  Δ tends to zero).

For a step index fibre operating at V=1.9, an 11% increase in Δ will cause a 5% increase in V, and reduce D by a factor 0.79, for a net reduction in waveguide dispersion by 8%.  If the dispersion zero wavelength is in the single mode region it will be shifted to shorter wavelengths.

In contrast, if Δ is increased, but the core size is reduced to keep V-number (and cut-off wavelength) constant, then the magnitude of waveguide dispersion will increase in proportion to Δ.  Zero dispersion wavelength in the single mode region will be shifted to longer wavelengths.

Note that dispersion depends on the second derivative of the propagation constant, and waveguide dispersion is rather sensitive to details of the refractive index profile.  Diffusion of dopants during fibre manufacture makes it difficult to achieve a perfect step index profile, especially for larger values of core refractive index.

More details including results for graded profile single mode fibres in A. W. Snyder & J. D. Love "Optical Waveguide Theory" (1983)  http://www.springer.com/gb/book/9780412099502

I also found the information but as you stated it is a mix of material dispersion and waveguide dispersion and explained separately I am now a bit more confidend of my answer and thinking direction. Thanks

good question, see this

super thanks!