diff --git a/src/graphs.jl b/src/graphs.jl
index 39c9d60ca..5d006641c 100644
--- a/src/graphs.jl
+++ b/src/graphs.jl
@@ -4,7 +4,7 @@ import Graphs
 function graphstate!(stab::Stabilizer)
     n = nqubits(stab)
     stab, r, s, permx, permz = canonicalize_gott!(stab)
-    perm = invperm(permx[permz])
+    perm = permx[permz]
     h_idx = [perm[i] for i in (r+1):n] # Qubits in which X ↔ Z is needed
     ip_idx = [perm[i] for i in 1:n if stab[i,i]==(true,true)] # Qubits for which Y → X is needed
     phase_flips = [perm[i] for i in 1:n if stab.phases[i]!=0x0]
diff --git a/test/test_graphs.jl b/test/test_graphs.jl
index 37406b16e..71a4e6af5 100644
--- a/test/test_graphs.jl
+++ b/test/test_graphs.jl
@@ -4,7 +4,6 @@ function test_graphs()
     @testset "Graph states" begin
         for n in [1,test_sizes...]
             s = random_stabilizer(n)
-            canonicalize_gott!(s)
             g, h_idx, ip_idx, z_idx = graphstate(s)
             gates = graph_gatesequence(h_idx, ip_idx, z_idx)
             gate = graph_gate(h_idx, ip_idx, z_idx, nqubits(s))
@@ -15,7 +14,22 @@ function test_graphs()
             for gate in vcat(gates...) apply!(s1, gate) end
             @test canonicalize!(apply!(copy(s),c0)) == canonicalize!(s1) == canonicalize!(Stabilizer(g))
         end
+        # one more check, done manually, to ensure we are testing for cases
+        # where canonicalize_gott! is causing index permutation
+        # (a few of the random cases already cover that)
+        s = S"- _XZ
+              + _ZX
+              + ZXZ"
+        g, h_idx, ip_idx, z_idx = graphstate(s)
+        gates = graph_gatesequence(h_idx, ip_idx, z_idx)
+        gate = graph_gate(h_idx, ip_idx, z_idx, nqubits(s))
+        c0 = one(CliffordOperator,nqubits(s))
+        for gate in vcat(gates...) apply!(tab(c0), gate) end
+        @test c0==gate
+        s1 = copy(s)
+        for gate in vcat(gates...) apply!(s1, gate) end
+        @test canonicalize!(apply!(copy(s),c0)) == canonicalize!(s1) == canonicalize!(Stabilizer(g))
     end
 end
 
-test_graphs()
\ No newline at end of file
+test_graphs()