This function returns the maximum number of independent vertices in a graph. This number can be found by computing the dimension of the simplicial complex whose faces are the independent sets (see independenceComplex) and adding 1 to this number.
i1 : R = QQ[a..e]; |
i2 : c4 = graph {a*b,b*c,c*d,d*a} -- 4-cycle plus an isolated vertex!!!!
o2 = Graph{edges => {{a, b}, {b, c}, {a, d}, {c, d}}}
ring => R
vertices => {a, b, c, d, e}
o2 : Graph
|
i3 : c5 = graph {a*b,b*c,c*d,d*e,e*a} -- 5-cycle
o3 = Graph{edges => {{a, b}, {b, c}, {c, d}, {a, e}, {d, e}}}
ring => R
vertices => {a, b, c, d, e}
o3 : Graph
|
i4 : independenceNumber c4 o4 = 3 |
i5 : independenceNumber c5 o5 = 2 |
i6 : dim independenceComplex c4 + 1 == independenceNumber c4 o6 = true |
The object independenceNumber is a method function.