2020/04/10 by Yuping Gao, Songling Shan, Gao, Yuping +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2004.05030
openalex publication_date 2020/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let m≥ 1 be an integer and G be a graph with m edges. We say that G has an antimagic orientation if G has an orientation D and a bijection τ:A(D)→ \1,2,⋯,m\ such that no two vertices in D have the same vertex-sum under τ, where the vertex-sum of a vertex u in D under τ is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Hefetz, Mütze and Schwartz [J. Graph Theory, 64: 219-232, 2010] conjectured that every connected graph admits an antimagic orientation. The conjecture was confirmed for certain classes of graphs such as dense graphs, regular graphs, and trees including caterpillars and k-ary trees. In this note, we prove that every lobster admits an antimagic orientation.