# An Algorithm for Constructing Graceful Tree from an Arbitrary Tree

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 246)

## Abstract

A function f is called graceful labeling of a graph G with m edges if f is an injective function from V(G) to {0, 1, 2, …, m} such that if every edge uv is assigned the edge label |f(u) − f(v)|, then the resulting edge labels are distinct. A graph that admits graceful labeling is called a graceful graph. The popular graceful tree conjecture states that every tree is graceful. The graceful tree conjecture remains open over four decades. In this paper, we introduce a new method of constructing graceful trees from a given arbitrary tree by designing an exclusive algorithm.

### Keywords

Graceful tree Graceful tree conjecture Graceful tree embedding Graceful labeling Graph labeling

## Notes

### Acknowledgments

The second author gratefully acknowledges Centre for Research, Anna University, Chennai, under the Grant Ref: CR/ACRF/Jan.2011/31.

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