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independenceNumber -- determines the independence number of a graph

Description

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

See also

Ways to use independenceNumber:

  • independenceNumber(Graph)

For the programmer

The object independenceNumber is a method function.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/EdgeIdeals.m2:2960:0.