Graceful Colorings of a Subclass of Bipartite Graphs

For \(X=\lbrace 1,2,\ldots ,l\rbrace \) , a graceful l-coloring of a graph G is a mapping of the vertices of the graph to the set X where the edge colors are the absolute difference between the colors of the end vertices satisfying the condition that every two adjacent vertices (edges) receive distinct colors. The least l for which G admits a graceful l-coloring is called the graceful chromatic number of G \((\chi _{g}(G))\) . The problem of computing the graceful chromatic number of bipartite graphs is still open. Hence, we pay attention to the computation of the graceful chromatic number of a subclass of bipartite graphs constructed using a graph operation named unfolding.