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Graphs and Combinatorics

, Volume 18, Issue 4, pp 795–802 | Cite as

On Non-Cayley Tetravalent Metacirculant Graphs

  • Ngo Dac Tan

Abstract.

 In connection with the classification problem for non-Cayley tetravalent metacirculant graphs, three families of special tetravalent metacirculant graphs, denoted by Φ1, Φ2 and Φ3, have been defined [11]. It has also been shown [11] that any non-Cayley tetravalent metacirculant graph is isomorphic to a union of disjoint copies of a non-Cayley graph in one of the families Φ1, Φ2 or Φ3. A natural question raised from the result is whether all graphs in these families are non-Cayley. We have proved recently in [12] that every graph in Φ2 is non-Cayley. In this paper, we show that every graph in Φ1 is also a connected non-Cayley graph and find an infinite class of connected non-Cayley graphs in the family Φ3.

Keywords

Classification Problem Natural Question Disjoint Copy Infinite Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 2002

Authors and Affiliations

  • Ngo Dac Tan
    • 1
  1. 1.Hanoi Institute of Mathematics, P.O. Box 631 Bo Ho, 10 000 Hanoi, Vietnam e-mail: ndtan@thevinh.ncst.ac.vnVN

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