Premium
Antimagic orientation of graphs with minimum degree at least 33
Author(s) -
Shan Songling
Publication year - 2021
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22721
Subject(s) - combinatorics , mathematics , bijection , bipartite graph , vertex (graph theory) , graph , orientation (vector space) , degree (music) , complete bipartite graph , edge graceful labeling , discrete mathematics , line graph , graph power , geometry , physics , acoustics
An antimagic labeling of a directed graph D with n vertices and m arcs is a bijection from the set of arcs of D to the integers { 1 , … , m } such that all n oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. A graph has an antimagic orientation if it has an orientation that admits an antimagic labeling. Hefetz, Mütze, and Schwartz conjectured that every connected graph admits an antimagic orientation. In this paper, we show that every bipartite graph with no vertex of degree 0 or 2 admits an antimagic orientation and every graph with minimum degree at least 33 admits an antimagic orientation.