# antiCycle -- returns a graph of an anticycle

## Synopsis

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

## Description

This function returns the graph that is the complement of the cycle obtained from L by applying the function cycle.

 i1 : R = QQ[a,b,c,d,e]; i2 : antiCycle R o2 = Graph{edges => {{a, c}, {a, d}, {b, d}, {b, e}, {c, e}}} ring => R vertices => {a, b, c, d, e} o2 : Graph i3 : antiCycle(R,4) o3 = Graph{edges => {{a, c}, {b, d}} } ring => R vertices => {a, b, c, d, e} o3 : Graph i4 : antiCycle {e,c,d,b} o4 = Graph{edges => {{d, e}, {b, c}} } ring => R vertices => {a, b, c, d, e} o4 : Graph i5 : complementGraph antiCycle R == cycle R o5 = true