diff --git a/sycl/source/detail/graph_impl.cpp b/sycl/source/detail/graph_impl.cpp
index 2581fb1da345f..bf69241266c28 100644
--- a/sycl/source/detail/graph_impl.cpp
+++ b/sycl/source/detail/graph_impl.cpp
@@ -724,11 +724,6 @@ void exec_graph_impl::createCommandBuffers(
 }
 
 exec_graph_impl::~exec_graph_impl() {
-  WriteLock LockImpl(MGraphImpl->MMutex);
-
-  // clear all recording queue if not done before (no call to end_recording)
-  MGraphImpl->clearQueues();
-
   const sycl::detail::PluginPtr &Plugin =
       sycl::detail::getSyclObjImpl(MContext)->getPlugin();
   MSchedule.clear();
diff --git a/sycl/source/detail/scheduler/commands.cpp b/sycl/source/detail/scheduler/commands.cpp
index 15741a11d5a2b..579d08a1c31fe 100644
--- a/sycl/source/detail/scheduler/commands.cpp
+++ b/sycl/source/detail/scheduler/commands.cpp
@@ -2488,8 +2488,9 @@ pi_int32 enqueueImpCommandBufferKernel(
   }
 
   if (Res != pi_result::PI_SUCCESS) {
-    throw sycl::exception(errc::invalid,
-                          "Failed to add kernel to PI command-buffer");
+    const device_impl &DeviceImplem = *(DeviceImpl);
+    detail::enqueue_kernel_launch::handleErrorOrWarning(Res, DeviceImplem,
+                                                        PiKernel, NDRDesc);
   }
 
   return Res;
diff --git a/sycl/test-e2e/Graph/Explicit/work_group_size_prop.cpp b/sycl/test-e2e/Graph/Explicit/work_group_size_prop.cpp
index 33b358a2e56db..cea6938cce300 100644
--- a/sycl/test-e2e/Graph/Explicit/work_group_size_prop.cpp
+++ b/sycl/test-e2e/Graph/Explicit/work_group_size_prop.cpp
@@ -5,8 +5,10 @@
 //
 // CHECK-NOT: LEAK
 
-// Note: failing negative test with CUDA & HIP in the original test
-// UNSUPPORTED: cuda, hip
+// Temporarily disabled for CUDA.
+// XFAIL: cuda
+// Note: failing negative test with HIP in the original test
+// TODO: disable hip when HIP backend will be supported by Graph
 
 #define GRAPH_E2E_EXPLICIT
 
diff --git a/sycl/test-e2e/Graph/Inputs/work_group_size_prop.cpp b/sycl/test-e2e/Graph/Inputs/work_group_size_prop.cpp
index 781aae21fb2d7..52efa89256ec1 100644
--- a/sycl/test-e2e/Graph/Inputs/work_group_size_prop.cpp
+++ b/sycl/test-e2e/Graph/Inputs/work_group_size_prop.cpp
@@ -85,8 +85,6 @@ int test(queue &Queue, PropertiesT Props, KernelType KernelFunc) {
     return 1;
   }
 
-  return 0;
-
   // Negative test case: Specify local size that does not match required size.
   exp_ext::command_graph GraphN{Queue.get_context(), Queue.get_device()};
   try {
diff --git a/sycl/test-e2e/Graph/RecordReplay/work_group_size_prop.cpp b/sycl/test-e2e/Graph/RecordReplay/work_group_size_prop.cpp
index 96445e6d514ee..5edef0355c57e 100644
--- a/sycl/test-e2e/Graph/RecordReplay/work_group_size_prop.cpp
+++ b/sycl/test-e2e/Graph/RecordReplay/work_group_size_prop.cpp
@@ -5,8 +5,10 @@
 //
 // CHECK-NOT: LEAK
 
-// Note: failing negative test with CUDA & HIP in the original test
-// UNSUPPORTED: cuda, hip
+// Temporarily disabled for CUDA.
+// XFAIL: cuda
+// Note: failing negative test with HIP in the original test
+// TODO: disable hip when HIP backend will be supported by Graph
 
 #define GRAPH_E2E_RECORD_REPLAY