Cycle Complement Graph

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CycleComplementGraph

The -cycle complement graph is the graph complement of the cycle graph . Cycle complement graphs are special cases of circulant graphs given by , where $S={j in Z:2<=j<=|_n/2_|}$ and denotes the floor function. The first few are illustrated above in embeddings obtained by removing a cycle from the complete graph (top) and in "standard" circulant graph form (bottom).

The wheel complement graph is isomorphic to the graph disjoint union of the cycle complement graph and singleton graph.

Special cases are summarized in the table below.

	graph name
3	empty graph
4	ladder rung graph
5	cycle graph
6	prism graph
7	circulant graph
8	circulant graph
9	circulant graph
10	circulant graph

See also

Cycle Graph, Graph Complement, Path Complement Graph, Wheel Complement Graph

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References

House of Graphs. Cycle Complement Graphs. Square of C_7, Complement of C_8, Cube of C_9, Circulant C_10 (1,2,4,5), Circulant C_11 (2,3,4,5), and others.

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Cycle Complement Graph

Cite this as:

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

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