Free objects of a band arising from graphs

The purpose of this paper is to present in contemporary terminology, a new approach to introduce free objects of a band, like free normal bands, free rectangular bands and free bands through graphs. The cardinalities of the free objects are also calculated, first for complete graphs. After removing of edges the resulting graphs become incomplete and regular. Green's relations for free objects are also discussed and explained by an egg-box diagram. They may provide a way for codes through graphs.