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A Flexible Edge Search Algorithm for Graceful Tree Labeling

Michael Arnold and Fabio Vitor

Abstract

Graceful labeling is a famous problem in graph theory. Conjecture says that all trees are graceful . The Edge Search Algorithm developed by Horton [16] can solve graceful labeling for unrooted trees. However, it cannot accurately solve graceful labeling for rooted trees. This paper presents the Flexible Edge Search Algorithm, which can quickly find a solution to the graceful labeling problem in rooted trees. In addition, it accurately finds which rooted trees are impossible to solve for. Computational experiments indicate that all such impossible roots are in trees of the same class: the scorpion. MSC Codes: 05C78, 05C05, 05C85

Keywords

Graceful LabelingRooted TreesGraph Algorithms

References

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