Antimagic Labeling of Regular Graphs |
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| Authors: | Feihuang Chang Yu‐Chang Liang Zhishi Pan Xuding Zhu |
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| Affiliation: | 1. DIVISION OF PREPARATORY PROGRAMS FOR OVERSEAS CHINESE STUDENTS, TAIWAN NORMAL UNIVERSITY, TAIPEI CITY, TAIWAN;2. DEPARTMENT OF APPLIED MATHEMATICS, NATIONAL PINGTUNG UNIVERSITY, PINGTUNG, TAIWAN;3. DEPARTMENT OF MATHEMATICS, TAMKANG UNIVERSITY, NEW TAIPEI CITY, TAIWAN;4. DEPARTMENT OF MATHEMATICS, ZHEJIANG NORMAL UNIVERSITY, JINHUA, CHINA |
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| Abstract: | A graph  is antimagic if there is a one‐to‐one correspondence  such that for any two vertices  ,  . 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. |
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| Keywords: | antimagic regular graph labeling |
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