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On \(\sigma \)-Tripartite Labelings of Odd Prisms and Even Möbius Ladders

  • Wannasiri WannasitEmail author
  • Saad El-Zanati
Article
  • 79 Downloads

Abstract

A common question in the study of graph decompositions is when does a graph G decompose the complete graph or the complete graph with a 1-factor removed or added. It is known that a \(\sigma \)-tripartite labeling of a tripartite graph G with n edges can be used to obtain a cyclic G-decomposition of \(K_{2nt+1}\) for every positive integer t. Moreover, it can be used to obtain a cyclic G-decomposition of both \(K_{2nt+2}-I\) and \(K_{2nt}+I\), where I is a 1-factor. We show that if G is an odd prism on 10 or more vertices or an even Möbius ladder, then G admits a \(\sigma \)-tripartite labeling.

Keywords

Cyclic G-designs Cubic Tripartite graphs \(\sigma \)-tripartite labelings 

Mathematics Subject Classification

05C78 

Notes

Acknowledgements

The authors wish to thank an anonymous referee for several helpful suggestions that improved the presentation of the results in this paper. This research was supported by the Thailand Research Fund (TRF) and Chiang Mai University, Grant No. TRG5880080.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of MathematicsChiang Mai UniversityChiang MaiThailand
  2. 2.Department of MathematicsIllinois State UniversityNormalUSA

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