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Cycle Complement Graph

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CycleComplementGraph

The n-cycle complement graph C^__n is the graph complement of the cycle graph C_n. Cycle complement graphs are special cases of circulant graphs given by Ci_n(1,2,...,|_n/2_|). The first few are illustrated above in embeddings obtained by removing a cycle from the complete graph K_n (top) and in "standard" circulant graph form (bottom).

The wheel complement graph W^__(n+1) is isomorphic to the graph disjoint union C^__n union K_1 of the cycle complement graph C^__n and singleton graph.

Special cases are summarized in the table below.

ngraph name
3empty graph K^__3
4ladder rung graph 2P_2
5cycle graph C_5
6prism graph P_2 square C_3
7circulant graph Ci_7(1,2)
8circulant graph Ci_8(1,2,4)
9circulant graph Ci_9(1,2,3)
10circulant graph Ci_(10)(1,2,4,5)

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 C7, Complement of C8, Cube of C9, Circulant C10 (1,2,4,5), Circulant C11 (2,3,4,5), Circulant C12 (1,2,3,4,6), Circulant C13 (1,2,3,4,5), C5, Empty graph on 3 vertices, 2K2, and K3 Box K2.

Referenced on Wolfram|Alpha

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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