Umm, no.
Carbon exists in several different forms: charcoal is nominally pure carbon but with impurities; diamond is mostly pure carbon in a face-centered cubic structure; “Buckyballs” are C-60 in a (kind of, if you squint) soccer-ball shape. Graphene is a *sheet* of carbon atoms. It can have a number of different oxygen-bearing substrates, e.g. carboxyl or hydroxyl groups, or even epoxides or carbonyl groups.
You’re thinking of what happens when you burn ordinary carbon in sufficient oxygen such that each carbon atom forms a product of carbon dioxide, a linear double-bonded molecule with carbon in the center, sigma and pi-bonding to the oxygens on either side.
I'm a science-minded fellow myself. I understand different molecular weights for a given element. I understand covalent and ionic bonding.
I just didn't know that people referred to graphene with the crystal lattice doped with oxygen as "graphene oxide". Silicon in semiconductors is not called anything goofy when doped with germanium or other elements to form the semiconductor.