isConnected(Poset) -- determines if a poset is connected

Synopsis

Function: isConnected
Usage:

i = isConnected P
Inputs:
- P, an instance of the type Poset,
Outputs:
- i, a Boolean value, whether $P$ is connected

Description

The poset $P$ is connected if the number of connectedComponents is $1$. Equivalently, the poset $P$ is connected if between every pair of vertices in $P$ there exists a chain of relations going from one to the other.

The divisorPoset of $n$ is always connected.

i1 : isConnected divisorPoset 18

o1 = true

The disjoint union of any two posets on disjoint vertex sets is disconnected.

i2 : C = chain 3;

i3 : P = sum(5, i -> naturalLabeling(C, 10*i));

i4 : isConnected P

o4 = false

Ways to use this method: