diff --git a/gap/semigroups/semigraph.gi b/gap/semigroups/semigraph.gi
index 551491f4e..8009e7e26 100644
--- a/gap/semigroups/semigraph.gi
+++ b/gap/semigroups/semigraph.gi
@@ -35,13 +35,18 @@ end);
 InstallMethod(AssignGeneratorVariables, "for an inverse semigroup",
 [IsGraphInverseSemigroup],
 function(S)
-  DoAssignGenVars(GeneratorsOfInverseSemigroup(S));
+  # the zero element uses the char 0, which cannot be assigned as a variable
+  if DigraphNrVertices(GraphOfGraphInverseSemigroup(S)) < 2 then
+    Info(InfoWarning, 1, "zero element is a generator but was not assigned!");
+  fi;
+  DoAssignGenVars(Difference(GeneratorsOfInverseSemigroup(S),
+    [MultiplicativeZero(S)]));
 end);
 
 InstallMethod(GraphInverseSemigroup, "for a digraph",
 [IsDigraph],
 function(graph)
-  local fam, S, gens, i;
+  local fam, S, gens, inv_gens, i;
 
   fam := NewFamily("GraphInverseSemigroupElementsFamily",
                    IsGraphInverseSemigroupElement,
@@ -66,15 +71,24 @@ function(graph)
   fam!.semigroup := S;
 
   gens := [];
+  inv_gens := [];
+  SetGraphOfGraphInverseSemigroup(S, graph);
+
   for i in [1 .. DigraphNrVertices(graph) + DigraphNrEdges(graph)] do
-    Add(gens, Objectify(fam!.type, [[i], graph]));
+    Add(inv_gens, Objectify(fam!.type, [[i], graph]));
   od;
-  SetGeneratorsOfSemigroup(S,
-                           Concatenation(gens,
-                                         List([1 .. DigraphNrEdges(graph)],
-                                              x -> gens[x] ^ -1)));
-  SetGeneratorsOfInverseSemigroup(S, gens);
-  SetGraphOfGraphInverseSemigroup(S, graph);
+
+  gens := Concatenation(inv_gens, List([1 .. DigraphNrEdges(graph)],
+            x -> inv_gens[x] ^ -1));
+
+  # if the graph has 0 or 1 vertex, then the zero element is not generated by
+  # products of vertices and edges, so must be added to both generating sets
+  if DigraphNrVertices(graph) < 2 then
+    Add(gens, MultiplicativeZero(S));
+    Add(inv_gens, MultiplicativeZero(S));
+  fi;
+  SetGeneratorsOfSemigroup(S, gens);
+  SetGeneratorsOfInverseSemigroup(S, inv_gens);
   return S;
 end);
 
@@ -286,7 +300,8 @@ InstallMethod(EdgesOfGraphInverseSemigroup,
 "for a graph inverse semigroup",
 [IsGraphInverseSemigroup],
 S -> Difference(GeneratorsOfInverseSemigroup(S),
-VerticesOfGraphInverseSemigroup(S)));
+Concatenation([MultiplicativeZero(S)],
+VerticesOfGraphInverseSemigroup(S))));
 
 InstallMethod(IndexOfVertexOfGraphInverseSemigroup,
 "for a graph inverse semigroup element",
diff --git a/tst/standard/semigroups/grpperm.tst b/tst/standard/semigroups/grpperm.tst
index 8b4151589..f6129b411 100644
--- a/tst/standard/semigroups/grpperm.tst
+++ b/tst/standard/semigroups/grpperm.tst
@@ -374,8 +374,8 @@ gap> iso := IsomorphismPermGroup(S);
 Error, the argument (a semigroup) does not satisfy IsGroupAsSemigroup
 
 # IsomorphismPermGroup: for a Integer Matrix Semigroup
-gap> S := GraphInverseSemigroup(Digraph([[]]));
-<finite graph inverse semigroup with 1 vertex, 0 edges>
+gap> S := GraphInverseSemigroup(Digraph([]));
+<finite graph inverse semigroup with 0 vertices, 0 edges>
 gap> iso := IsomorphismPermGroup(S);;
 gap> BruteForceIsoCheck(iso); BruteForceInverseCheck(iso);
 true
diff --git a/tst/standard/semigroups/semirms.tst b/tst/standard/semigroups/semirms.tst
index 92de348bc..5acce64be 100644
--- a/tst/standard/semigroups/semirms.tst
+++ b/tst/standard/semigroups/semirms.tst
@@ -1912,8 +1912,8 @@ true
 
 # AsSemigroup: 
 #   convert from IsGraphInverseSemigroup to IsReesMatrixSemigroup
-gap> S := GraphInverseSemigroup(Digraph([[]]));
-<finite graph inverse semigroup with 1 vertex, 0 edges>
+gap> S := GraphInverseSemigroup(Digraph([]));
+<finite graph inverse semigroup with 0 vertices, 0 edges>
 gap> T := AsSemigroup(IsReesMatrixSemigroup, S);
 <Rees matrix semigroup 1x1 over Group(())>
 gap> Size(S) = Size(T);