The rattle graph is the union of two graphs. The rattle or bulb part of the graph is simply an n-cycle. This n cycle is joined to a stem or handle of a rattle of length k, so the second piece is just a path graph on k vertices.
i1 : rattleGraph (6, 3)
o1 = Graph{0 => {1, 5} }
1 => {0, 2}
2 => {1, 3}
3 => {2, 4}
4 => {3, 5}
5 => {0, 4, 6}
6 => {5, 7}
7 => {6, 8}
8 => {7}
o1 : Graph
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The object rattleGraph is a method function.