On the enumeration of a class of toroidal graphs
DOI:
https://doi.org/10.11575/cdm.v13i1.62310Keywords:
Toroidal Graphs, Semi-Equivelar Maps, CyclesAbstract
We present enumerations of a class of toroidal graphs which are called semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eight non-isomorphic types of semi-equivelar maps on the torus: $\{3^{3}, 4^{2}\}$, $\{3^{2}, 4, 3, 4\}$, $\{3, 6, 3, 6\}$, $\{3^{4}, 6\}$, $\{4, 8^{2}\}$, $\{3, 12^{2}\}$, $\{4, 6, 12\}$, $\{3, 4, 6, 4\}$. We attempt to classify all these maps.References
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U. Brehm and E. Schulte, Handbook of discrete and computational geometry, ch. Polyhedral maps, pp. 345-358, CRC Press, NY, 1997.
W. Kurth, Enumeration of platonic maps on the torus, Discrete Math. 61 (1986), 71-83.
S. Negami, Uniqueness and faithfulness of embedding of toroidal graphs, Discrete Math. 44 (1983), 161-180.
A. K. Tiwari and A. K. Upadhyay, An enumeration of semi-equivelar maps on torus and klein bottle, to appear.
A. K. Upadhyay, A. K. Tiwari, and D. Maity, Semi-equivelar maps, Beitr. Algebra Geom. 55 (2014), 229-242.
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