TOPICS
Tietze Graph
The Tietze graph is the cubic graph on 12 nodes and 18 edges, illustrated above in a number of embeddings.
It is implemented in the Wolfram Language as GraphData["TietzeGraph"].
The Tietze graph is the unique almost Hamiltonian cubic graph on 12 vertices (Punnim et al. 2007). In fact, it is also maximally nonhamiltonian (Clark and Entringer 1983) and a platypus graph.
The Tietze graph provides a 6-color coloring of the Möbius strip as illustrated above (Bondy and Murty 1976, p. 243).
The plots above show the adjacency, incidence, and graph distance matrices for the Tietze graph.
See also
Cubic Graph, Möbius StripExplore with Wolfram|Alpha
References
Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 243, 1976.Clark, L. and Entringer, R. "Smallest Maximally Nonhamiltonian Graphs." Periodica Math. Hungarica 14, 57-68, 1983.Goedgebeur, J.; Neyt, A.; and Zamfirescu, C. T. "Structural and Computational Results on Platypus Graphs." Appl. Math. Comput., 386:125491, 10 pages, 2020.House of Graphs. "Tietzes Graph." https://houseofgraphs.org/graphs/1368.HousePunnim, N.; Saenpholphat, V.; and Thaithae, S. "Almost Hamiltonian Cubic Graphs." Int. J. Comput. Sci. Netw. Security 7, 83-86, 2007.Cite this as:
Weisstein, Eric W. "Tietze Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TietzeGraph.html