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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Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of MathematicsAnna UniversityChennaiIndia

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