Antimagic Labeling of Regular Graphs

A graph G=(V,E) is antimagic if there is a one‐to‐one correspondence f:E→{1,2,...,|E|} such that for any two vertices u,v, ∑e∈E(u)f(e)≠∑e∈E(v)f(e). It is known that bipartite regular graphs are antimagic and nonbipartite regular graphs of odd degree at least three are antimagic. Whether all nonbipar...

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Bibliographic Details
Published inJournal of graph theory Vol. 82; no. 4; pp. 339 - 349
Main Authors Chang, Feihuang, Liang, Yu-Chang, Pan, Zhishi, Zhu, Xuding
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.08.2016
Wiley Subscription Services, Inc
Subjects
antimagic
Graphs
labeling
regular graph
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Summary:A graph G=(V,E) is antimagic if there is a one‐to‐one correspondence f:E→{1,2,...,|E|} such that for any two vertices u,v, ∑e∈E(u)f(e)≠∑e∈E(v)f(e). It is known that bipartite regular graphs are antimagic and nonbipartite regular graphs of odd degree at least three are antimagic. Whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. In this article, we solve this problem and prove that all even degree regular graphs are antimagic.
Bibliography:ark:/67375/WNG-90T4X9BN-0
istex:73C48EDC17852F529AA2CDD85D2AEA2EDC0BE027
ArticleID:JGT21905
Contract grant number: NSC 102‐2115‐M‐003‐008
Contract grant number: MOST 104‐2811‐M‐153‐001
Contract grant number: NSC 102‐2115‐M‐032 ‐006
Contract grant number: CNSF11171310.
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.21905