-- -*- M2-comint -*- {* hash: -683691469 *}

i1 : R = QQ[x_1..x_6];

i2 : G = graph({x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_5,x_1*x_5,x_1*x_6,x_5*x_6}) --5-cycle and a triangle

o2 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
                       1   2     2   3     3   4     1   5     4   5     1   6     5   6
           ring => R
           vertices => {x , x , x , x , x , x }
                         1   2   3   4   5   6

o2 : Graph

i3 : numTriangles G

o3 = 1

i4 : H = completeGraph R;

i5 : numTriangles H == binomial(6,3)

o5 = true

i6 :