Antimagic orientations for the complete k -ary trees
Journal of Combinatorial Optimization(2019)
摘要
labeling of a digraph D with m arcs is a bijection from the set of arcs of D to {1,2,… ,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 ∈ 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 .
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关键词
Complete k-ary tree, Antimagic labeling, Antimagic orientation
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