GAP:DirectedPowerGraph

This article is about a GAP function.

This GAP function takes as input a group. See more functions like this.

Definition

Function type

The function takes as input a group (supposed to be a finite group) and outputs a graph.

Behavior

The graph output is isomorphic to the directed power graph of the group.

Packages used

The function definition requires the Grape package. If this package is installed but not loaded, it can be loaded using:

LoadPackage("grape")

Method

Code

DirectedPowerGraph := function(G)
        local L,o,f;
        o := Order(G);
        L := AsList(Set(G));
        f := function(x,y)
                return(IsSubgroup(Group(L[x]),Group(L[y])));
        end;;
        return(Graph(TrivialSubgroup(SymmetricGroup(o)),[1..o],OnPoints,f,true)\
);