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An -gonal -cone graph, also called the -point suspension of or generalized wheel graph (Buckley and Harary 1988), is defined by the graph join , where is a cycle graph and is an empty graph (Gallian 2026), with integers and .

Special cases are summarized in the following table.

Buckley and Harary (1988) consider the graph dimension of the cone graph.

Precomputed properties of cone graphs are implemented in the Wolfram Language as GraphData[{"Cone", {m, n}}].

Embeddings of a number of small cone graphs are illustrated above.

See also

Complete Tripartite Graph, Dipyramidal Graph, Graph Join, k-Tree, Wheel Graph

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References

Buckley, F. and Harary, F. "On the Euclidean Dimension of a Wheel." Graphs and Combin. 4, 23-30, 1988. https://doi.org/10.1007/BF01864150.Gallian, J. A. §2.2 in "A Dynamic Survey of Graph Labeling." Elec. J. Combin., Dynamic Survey DS6, Nov. 6, 2026. https://doi.org/10.37236/27.House of Graphs. Cone Graphs. Tetrahedron K_4, Wheel W_5, Wheel W_6, Wheel W_7, Wheel W_8, and others.

Referenced on Wolfram|Alpha

Cone Graph

Cite this as:

Weisstein, Eric W. "Cone Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConeGraph.html

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