antiCycle -- returns a graph of an anticycle

• 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, a graph, an anticycle on the vertices in L or on the variables of R.

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