isLeaf -- determines if an edge (or vertex) is a leaf of a (hyper)graph

Synopsis

Usage:

b = isLeaf(G,N)

b = isLeaf(H,n)

b = isLeaf(H,V)
Inputs:
- G, a graph,
- H, a hypergraph,
- n, an integer, an index of an edge
- V, a ring element, a vertex
Outputs:
- b, a Boolean value, true if edge n is a leaf or if vertex V has degree 1

Description

An edge in a graph is a leaf if it contains a vertex of degree one. An edge E in a hypergraph is a leaf if there is another edge B with the property that for all edges F (other than E), the intersection of F with E is contained in the intersection of B with E.

A vertex of a graph is a leaf if it has degree one. A vertex of a hypergraph is a leaf if it is contained in precisely one edge which is itself is leaf.

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

i2 : G = graph {a*b,b*c,c*a,b*d};

i3 : isLeaf(G, d)

o3 = true

i4 : isLeaf(G, getEdgeIndex(G, {b,d}))

o4 = true

i5 : isLeaf(G, a)

o5 = false

i6 : isLeaf(G, getEdgeIndex(G, {a,b}))

o6 = false

i7 : H = hyperGraph {a*b*c,b*d,c*e,b*c*f};

i8 : K = hyperGraph {a*b*c,b*d,c*e};

i9 : isLeaf(H, a)

o9 = true

i10 : isLeaf(H, getEdgeIndex(H, {a,b,c}))

o10 = true

i11 : isLeaf(K, a)

o11 = false

i12 : isLeaf(K, getEdgeIndex(K, {a,b,c}))

o12 = false

Ways to use isLeaf :

isLeaf(Graph,ZZ)
isLeaf(HyperGraph,RingElement)
isLeaf(HyperGraph,ZZ)

For the programmer

The object isLeaf is a method function.

isLeaf -- determines if an edge (or vertex) is a leaf of a (hyper)graph

Synopsis

Description

See also

Ways to use isLeaf :

For the programmer