yes but how? is it for single atom thickness, but how much conductivity for graphene 1000000 times as compared to graphite(1000) 

Some data on both systems are available in the following paper by Balandin et al.

Depends. It is true that graphene is known to show very high carrier mobilities and and conductivity etc, but this is only on very small samples where there are very few (if any at all) grain boundaries. Compared to CVD grown graphene over several 10s of microns (at least), graphite would be better.

In single wall there will be no electron scattering  as compared to graphite which is multilateral where electron mobility has been impeded.So that conductivity would become lower.   

Graphene is more conductance than graphite, I think because the band gab less 

graphen is more conductive than graphite because of its single layer construction and higher electron mobility

The conductivity of graphene can be increased through doping, 

Graphene is highly sensitive to the environment. There are several that can improve the performance of your device like suspending it or place it on a very flat surface like BN. If you deal with CVD grown graphene, it's favorable to use single grain graphene. Check my paper on graphlocons.

Article Quantum Hall effect in fractal graphene: Growth and properti...

Try to do doping. As by simulation I have checked that we  can shift the point where the conduction and valence bands meets by the type of doping.

I think it will be useful if you try to fictionalize it with conductive materials such as gold.

@Ali Fazil.gold etc reduces conductivity of graphene.They quench it.

you could increase the graphene conductivity by metal or metal oxide functionality. Recently, we have seen Mn3O4 and Fe3O4 are incorporated with graphene to enhance the electron flux.