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On the Möbius Ladders

  • Richard K. Guy (a1) and Frank Harary (a2)
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Consider the graph Mn, where n = 2r ≥ 6, consisting of a polygon of length n and all n/2 chords joining opposite pairs of vertices. This graph has 2r vertices which we denote by 1, 2, 3,..., 2r, and the 3r (undirected) edges

We call Mn the n-ladder, defined thus far only for n even. The three smallest n-ladders with n even are shown in Figure 1.

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References
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1. Guy, R. K., A combinatorial problem. Bull. Malayan Math. Soc. 7 (1966), 68-72.
2. Harary, F., On minimally nonplanar graphs. Ann. Univ. Sci. Budapest. Eótvós Sec. Math. 8 (1966), 13-15.
3. Harary, F. and Hill, A., On the number of crossings in a complete graph. Proc. Edinburgh Math. Soc. 13 (1966), 333-338.
4. Kuratowski, K., Sur le problème des courbesgauches en topologie. Fund. Math. 15 (1933), 271-283.
5. Zeeman, E. C., Unknotting 2-spheres in 5 dimensions. Bull. Amer. Math. Soc. 66 (1960), 198.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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