Journal of Applied Mathematics and Computing

, Volume 29, Issue 1–2, pp 105–116 | Cite as

On the odd harmonious graphs with applications

  • Zhi-He LiangEmail author
  • Zhan-Li Bai


The necessary conditions for the existence of odd harmonious labelling of graph are obtained. A cycle C n is odd harmonious if and only if n≡0 (mod 4). A complete graph K n is odd harmonious if and only if n=2. A complete k-partite graph K(n 1,n 2,…,n k ) is odd harmonious if and only if k=2. A windmill graph K n t is odd harmonious if and only if n=2. The construction ways of odd harmonious graph are given. We prove that the graph i=1 n G i , the graph G(+r 1,+r 2,…,+r p ), the graph \(\bar{K_{m}}+_{0}P_{n}+_{e}\bar{K_{t}}\) , the graph G∪(X+∪ k=1 n Y k ), some trees and the product graph P m ×P n etc. are odd harmonious. The odd harmoniousness of graph can be used to solve undetermined equation.


Odd harmonious graph Harmonious graph Tree Product graph 

Mathematics Subject Classification (2000)



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Copyright information

© Korean Society for Computational and Applied Mathematics 2008

Authors and Affiliations

  1. 1.Department of MathematicsHebei Normal UniversityShijiazhuangPeople’s Republic of China
  2. 2.Editorial Department of Hebei Normal University JournalShijiazhuangPeople’s Republic of China

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