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Wreath Graph

The wreath graph W(n,k) is the graph obtained by taking n collections of k nodes and arranging around a circle such that all nodes in adjacent collections are connected. Wreath graphs are therefore a subset of circulant graphs (so all wreath graphs are circulant, though the converse does not hold) as summarized in the following table.

(n,k)graph
(n,1)cycle graph C_n
(n,3)circulant graph Ci_(2n)(1,n-1)
(n,4)circulant graph Ci_(3n)(1,n-1,n+1)
(n,5)circulant graph Ci_(4n)(1,n-1,n+1,2n-1)
(n,6)circulant graph Ci_(5n)(1,n-1,n+1,2n-1,2n+1)

Special cases by k are summarized in the following table.

(n,k)graph
(3,k)complete tripartite graph K_(k,k,k)
(4,k)complete bipartite graph K_(2k,2k)

See also

Circulant Graph

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Cite this as:

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

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