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ABSTRACT

Graceful labeling is one of the topics of graph theory which has been many researched. Graph  is called a graceful graph if the graph  has a graceful labeling. The graceful labeling of graph  with  edges is an injective mapping that satisfies  then every edge  is labeled with  and each edge label has a different value.

In 2009 Lu used Θ to denote the graph made from  copies of  (cycle that has  verteies) that share an edge. In this paper, we show that graph Θ is a graceful graph.

 

The procedure for doing the graceful labeling for  the graph Θcan be seen in Table 1.

 

Table 1. Labeling procedure for the graph Θ.

 

Step

Procedure

1

Label vertex  with

2

Label vertex  with 1

2

Label vertex  with ,

 

 

Figure 1. Graceful labeling for graph Θ.

Based on Figure 1 we can conclude that graph Θ is a graceful graph.

Graceful graph; Graceful labeling; Edge amalgamation of cycle graph