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Antimagic orientations for the complete k-ary trees

  • Chen Song
  • Rong-Xia HaoEmail author
Article
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Abstract

A labeling of a digraph D with m arcs is a bijection from the set of arcs of D to \(\{1,2,\ldots ,m\}\). A labeling of D is antimagic if all vertex-sums of vertices in D are pairwise distinct, where the vertex-sum of a vertex \(u \in V(D)\) for a labeling is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Hefetz et al. (J Graph Theory 64:219–232, 2010) conjectured that every connected graph admits an antimagic orientation. We support this conjecture for the complete k-ary trees and show that all the complete k-ary trees \(T_k^r\) with height r have antimagic orientations for any k and r.

Keywords

Complete k-ary tree Antimagic labeling Antimagic orientation 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11731002), the Fundamental Research Funds for the Central Universities (Nos. 2016JBM071, 2016JBZ012).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiaotong UniversityBeijingPeople’s Republic of China

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