GAP Manual: 58.27. IsConnectedGraph

IsConnectedGraph( gamma )

This boolean function returns true if and only if gamma is (strongly) connected, i.e. if there is a (directed) path from x to y for every pair of vertices x,y of gamma.

    gap> IsConnectedGraph( JohnsonGraph(4,2) );
    true
    gap> IsConnectedGraph( NullGraph(SymmetricGroup(4)) );
    false