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# cycle -- returns a graph cycle

## Synopsis

• Usage:
C = cycle R
C = cycle(R,n)
C = cycle L
• Inputs:
• R, a ring,
• n, an integer, length of cycle
• L, a list, of vertices to make into a cycle in the order provided
• Outputs:
• C, , a cycle on the vertices in L or on the variables of R.

## Description

Give a list of vertices (perhaps in some specified order), this function returns the graph of the cycle on those vertices, using the order given or the internal ordering of the vertices. Unspecified vertices are treated as isolated vertices.

 i1 : R = QQ[a,b,c,d,e]; i2 : cycle R o2 = Graph{"edges" => {{a, b}, {b, c}, {c, d}, {d, e}, {a, e}}} "ring" => R "vertices" => {a, b, c, d, e} o2 : Graph i3 : cycle(R,3) o3 = Graph{"edges" => {{a, b}, {b, c}, {a, c}}} "ring" => R "vertices" => {a, b, c, d, e} o3 : Graph i4 : cycle {e,c,d,b} o4 = Graph{"edges" => {{c, e}, {c, d}, {b, d}, {b, e}}} "ring" => R "vertices" => {a, b, c, d, e} o4 : Graph i5 : R = QQ[a,c,d,b,e];-- variables given different order i6 : cycle R o6 = Graph{"edges" => {{a, c}, {c, d}, {d, b}, {b, e}, {a, e}}} "ring" => R "vertices" => {a, c, d, b, e} o6 : Graph