Graphene is a novel material, but I can't see how you'd make a ring out of it.
Graphite (pencil lead) is the thermodynamically most stabile structure of pure carbon under normal atmospheric conditions, as opposed to diamond. It consists of layer upon layer of graphene, stacked atop of one another while not entirely bonding between the layers. For instance, while the material of graphene is very excellent at conducting electricity, graphite is only so in two directions. If you try to jump between graphene layers, you will not be able to conduct electricity.
Imagine graphene as a piece of paper, and then graphite as a book.
While graphene is a novel property, most of the novelty comes from the fact that it is an entirely two-dimensional structure, always flat, and always one carbon atom thick.
I would find it highly difficult to construct a ring of a one-atom thick sheet of paper. Should it be possible, the ring would probably be impossible to see with the naked eye, and incredibly fragile. Should you choose to make the ring bigger, so as to make it more sturdy, you would end up with a ring of graphite, i.e. pencil lead. You might convince your fiancee that if she jumped into a volcano, she might some day turn it into diamond. However I think most of the novelty will wear off as the ring will snap and draw on stuff.
If you want to incorporate graphene into a ring through some other measure... Well, you would have an impossibly thin and invisible layer on your ring. If you want to size it up, you will get a practical wedding ring which you can write "I love you" with for a few weeks.