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.
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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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Sethuraman, G., Ragukumar, P. (2014). An Algorithm for Constructing Graceful Tree from an Arbitrary Tree. In: Krishnan, G., Anitha, R., Lekshmi, R., Kumar, M., Bonato, A., Graña, M. (eds) Computational Intelligence, Cyber Security and Computational Models. Advances in Intelligent Systems and Computing, vol 246. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1680-3_29
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DOI: https://doi.org/10.1007/978-81-322-1680-3_29
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