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# coverIdeal -- Returns the vertex cover ideal of a graph

- Usage:
    `J = coverIdeal G`
- Inputs:
  - G, a graph,
- Outputs:
  - J, an ideal, The vertex cover ideal of a graph G

## Description

The vertex cover ideal of a graph G is the ideal generated by (m_s | s in [n] is a vertex cover of G), where m_s = product_(i in S)(x_i)

    i1 : G = graph({{1, 2}, {1, 3}, {2, 3}, {3, 4}},EntryMode=>"edges");

    i2 : coverIdeal G

    o2 = monomialIdeal (x x , x x , x x x )
                         1 3   2 3   1 2 4

    o2 : MonomialIdeal of QQ[x ..x ]
                              1   4

## See also

- edgeIdeal -- returns the edge ideal of a graph
- vertexCovers -- returns a list of the minimal vertex covers of a graph
- vertexCoverNumber -- returns the vertex cover number of a graph

## Ways to use coverIdeal:

- `coverIdeal(Graph)`

## For the programmer

The object coverIdeal is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Graphs.m2:3247:0.