Research Article

# On the Construction of the Reflexive Vertex -Labeling of Any Graph with Pendant Vertex

## Algorithm 1

The vertices’ and edges’ labels.
 (1) Define , and injecton for labeling of the graph elements (2) Assign the labels of vertices and edges of pendants according to Theorem 1. (3) Observe that the vertex weight on each pendant will be or . (8) The vertex weights of point (4),(7) are , but 5, 6 are respectively is and . Since the number of pendant vertices is , it will exist two type of vertices which have the same weights. Do the following. (9) When is even and is odd, add the label of each vertex or edge by 1. (10) Apart from pendants, assign the label of vertices as the label of pendant vertices , but the labels of edges with , thus the vertex weights are or . (11) Observe, all pendant vertices and otherwise show a different vertex weight. (11) STOP.

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