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# isGoodLeaf -- determines if an edge is a good leaf

- Usage:
    `b = isGoodLeaf(H,n)`
- Inputs:
  - H, a hypergraph,
  - n, an integer, index of an edge
- Outputs:
  - b, a Boolean value, true if edge n of H is a good leaf

## Description

A good leaf of hypergraph H is an edge L whose intersections with all other edges form a totally ordered set. It follows that L must have a free vertex. In the graph setting, a good leaf is an edge containing a vertex of degree one. The notion of a good leaf was introduced by X. Zheng in her Ph.D. thesis (2004).

    i1 : R = QQ[a..g];

    i2 : H = hyperGraph {a*b*c*d, b*c*d*e, c*d*f, d*g, e*f*g};

    i3 : edges(H)

    o3 = {{a, b, c, d}, {b, c, d, e}, {c, d, f}, {d, g}, {e, f, g}}

    o3 : List

    i4 : isGoodLeaf(H,0)

    o4 = true

    i5 : isGoodLeaf(H,1)

    o5 = false

## See also

- getGoodLeaf -- returns an edge that is a good leaf
- getGoodLeafIndex -- returns the index of an edge that is a good leaf
- hasGoodLeaf -- determines if a HyperGraph contains a good leaf

## Ways to use isGoodLeaf:

- `isGoodLeaf(HyperGraph,ZZ)`

## For the programmer

The object isGoodLeaf is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/EdgeIdeals.m2:3391:0.