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Regular Graphs of Odd Degree Are Antimagic
Author(s) -
Cranston Daniel W.,
Liang YuChang,
Zhu Xuding
Publication year - 2015
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.21836
Subject(s) - combinatorics , mathematics , bijection , conjecture , graph , degree (music) , edge graceful labeling , discrete mathematics , line graph , graph power , physics , acoustics
An antimagic labeling of a graph G with m edges is a bijection from E ( G ) to { 1 , 2 , ... , m } such that for all vertices u and v , the sum of labels on edges incident to u differs from that for edges incident to v . Hartsfield and Ringel conjectured that every connected graph other than the single edge K 2 has an antimagic labeling. We prove this conjecture for regular graphs of odd degree.