A polyhedral 9-vertex graph is a polyhedral graph on nine vertices . There are 2606 nonisomorphic
polyhedral 9-vertex graphs, corresponding through duality
to the convex enneahedra enumerated by Federico (1969).
Duijvestijn and Federico (1981) tabulate the counts by vertex
count and number of faces .
Named polyhedral 9-vertex graphs include the Fritsch graph , Soifer graph , and 9-wheel
graph skeletons
of Johnson solids 3, 8, 10, and 63, the fan graph , and the (3,3)-prism graph .
The name "nonahedral graph" is also used for this class (Gayathri 2018, p. 50; Daoud 2020).
See also Enneahedron ,
Nonahedral
Graph ,
Polyhedral Graph
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References Daoud, S. N. "Number of Spanning Trees in the Sequence of Some Nonahedral Graphs." Util. Math. 115 , 39-56, 2020.
https://utilitasmathematica.com/index.php/Index/article/view/1498 . Duijvestijn,
A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected
Planar) Graphs." Math. Comput. 37 , 523-532, 1981. https://doi.org/10.1090/S0025-5718-1981-0628713-3 . Federico,
P. J. "Enumeration of Polyhedra: The Number of 9-Hedra." J. Combin.
Th. 7 , 155-161, 1969. https://doi.org/10.1016/S0021-9800(69)80050-5 . Gayathri,
A. "A Study on Higher Order Triangular Sum Numbers of Polyhedral and Graceful
Graphs." Math. Sci. Internat. Res. J. 7 , 48-55, 2018. https://kanchiuniv.ac.in/wp-content/uploads/2022/02/Research-Compendium-2018.pdf . House
of Graphs. Polyhedral 9-Vertex Graphs. Fritsch
Graph , Soifer Graph , Wheel
W_9 , and others.
Cite this as:
Weisstein, Eric W. "Polyhedral 9-Vertex Graph."
From MathWorld https://mathworld.wolfram.com/Polyhedral9-VertexGraph.html
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Other polyhedral 9-vertex graphs include the skeletons
of Johnson solids 3, 8, 10, and 63, the 
-fan graph, and the (3,3)-prism graph.
