diff --git a/src/graph/graph.hh b/src/graph/graph.hh
index e9d20e1d1..85d71b418 100644
--- a/src/graph/graph.hh
+++ b/src/graph/graph.hh
@@ -415,6 +415,8 @@ namespace spot
       // Transition number 0 is not used, because we use this index
       // to mark the absence of a transition.
       transitions_.resize(1);
+      // This causes transition 0 to be considered as dead.
+      transitions_[0].next_succ = 0;
     }
 
     unsigned num_states() const
@@ -604,7 +606,7 @@ namespace spot
       return transitions_[t].next_succ == t;
     }
 
-    bool is_dead_transition(trans_storage_t& t) const
+    bool is_dead_transition(const trans_storage_t& t) const
     {
       return t.next_succ == index_of_transition(t);
     }
diff --git a/src/tgba/tgbagraph.hh b/src/tgba/tgbagraph.hh
index 0750d24ba..5d44878b5 100644
--- a/src/tgba/tgbagraph.hh
+++ b/src/tgba/tgbagraph.hh
@@ -361,8 +361,7 @@ namespace spot
     auto transitions()
       SPOT_RETURN(g_.transitions());
 
-    template<typename T>
-    auto is_dead_transition(T t) const
+    auto is_dead_transition(const graph_t::trans_storage_t& t) const
       SPOT_RETURN(g_.is_dead_transition(t));
 
     /// \brief Copy the acceptance conditions of another tgba.