A pretzel graph is a graph with graph genus 3 (West 2000, p. 266). Planar, toroidal
graphs, and double-toroidal graphs are
therefore not pretzel.
Examples of pretzel graphs include the complete graph 
and complete
bipartite graph 
.
There are no pretzel graphs on 8 or fewer nodes (E. Weisstein, Dec. 12, 2020).
See also
Double-Toroidal Graph,
Graph Genus,
Planar Graph,
Toroidal Graph
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References
West, D. B. "Surfaces of Higher Genus." Introduction
to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 266-269,
2000.
Cite this as:
Weisstein, Eric W. "Pretzel Graph." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PretzelGraph.html
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