Volume 1, Issue 1, August 2017, pp 7-22

## Graceful Labeling for different path and complete Bi-partite using Padavon sequence

A.Neerajah ^{1} and P.Subramanian^{2}

^{1}Department of Mathematics, Karpagam University, Coimbatore-641021, India.

^{2}Department of Mathematics, Government Arts College, Coimbatore-641018, India.

### Abstract

A path of length n is denoted by P_{n}. A function f is a graceful labeling of a graph G with p vertices and q edges, if f is injection from the vertices of G to the set {1 , 2 , … , q} such that when each edge uv is assigned the label |f(u)-f(v)| is distinct. In this paper, the gracefulness of padavon sequence for paths P_{n} for n=1 to 3 is obtained and gracefulness of padavon sequence for paths with two pendent vertices P_{n} for n=1 to 5 and complete bi-partite are obtained.

### Keywords

Complete bipartite, Graceful labeling, path, padavon sequence.

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