Are vg uuid unique ?
 

I tried to search for the answer in various posts but to no avail.

1) vg uuid generated on a single node seems to be unique. Please confirm.

2) But in a cluster (that has a shared storage) can the vg UUID be different for a shared vg containing same pvs ?.

What you mean with 'vg' and 'pvs'? If you mean the disks' UUID is surely unique (UUID means 'universally unique identifier'), but I suggest you to use labels instead UUIDs. They are more friendly and you can use them like UUIDs: for example, for mounting a FAT16 device, that you call "pendrive", in a directory called /media/pendrive, you can run from terminal:

1) Read the description in the manpage for uuidgen.
2) The uuid is generated once - when the vg is created. It will be common, and is part of the meta-data read at boot/mount time