On Graceful Labeling of Some Graphs with Pendant Edges

A graceful labeling of a graph G of size q is an injective assignment of labels from the set {0,1,...,q} to the vertices of G such that when each edge of G has been assigned a label defined by the absolute difference of its end-vertices, the resulting edge labels are distinct. In this paper we have shown that the graphs which are obtained by adding the pendant edges to the vertices of K sub n /sub or P sub 2 /sub or both in P sub 2 /sub K sub n /sub are graceful. We have also shown that the graph which obtains by adding one pendant edge to each pendant vertices of C sub n /sub ʘ 1K sub 1 /sub , n ≡ 3 mod (4) is graceful.