Number of free electron(s) in each carbon atom in graphite is/are:
1
Carbon has four valence electrons. In the graphite structure, each carbon atom is bonded with three other carbon atoms by a single covalent bond in a honeycomb structure. Therefore, one electron is not bonded to any other carbon atom. This free electron gives graphite the ability to conduct electricity. Since these electrons do not have a fixed location in the structure of graphite, they are called delocalised electrons. You can see in the image below if we take only one layer of graphite how each carbon atom is bonded with three carbon atoms only.
Note: Every tiny sphere in the image is a carbon atom and the lines connecting them represent a single covalent bond.