The  centered hexagonal number is denoted by and is of the form .  Let  be a graph. Let and denote the vertex set and the edge set of  respectively. A centered hexagonal graceful labeling of a graph  is an one to one function that induces a bijection of the edges of  defined by . The graph which admits such a labeling is called a centered hexagonal graceful graph. In this paper, centered hexagonal graceful labeling of caterpillar and uniform caterpillar graphs are studied. 

Keywords:  centered hexagonal numbers, centered hexagonal labeling, centered hexagonal graceful graph.