diff --git a/elyra/pipeline/pipeline.py b/elyra/pipeline/pipeline.py
index e583d993e..e428b6b5c 100644
--- a/elyra/pipeline/pipeline.py
+++ b/elyra/pipeline/pipeline.py
@@ -336,7 +336,7 @@ def gpu_vendor(self) -> Optional[str]:
 
     @property
     def parallel_count(self) -> Optional[str]:
-        return self._component_props.get("parallel_count")
+        return self._component_props.get("parallel_count", 1)
 
     def __eq__(self, other: GenericOperation) -> bool:
         if isinstance(self, other.__class__):
diff --git a/elyra/templates/kubeflow/v1/python_dsl_template.jinja2 b/elyra/templates/kubeflow/v1/python_dsl_template.jinja2
index 1904d5f57..9ebce539c 100644
--- a/elyra/templates/kubeflow/v1/python_dsl_template.jinja2
+++ b/elyra/templates/kubeflow/v1/python_dsl_template.jinja2
@@ -34,10 +34,12 @@ def generated_pipeline(
     {% set task_name = "task_" + workflow_task.escaped_task_id %}
     # Task for node '{{ workflow_task.name }}'
     {% set parallel_indent = 0 %}
-{%  if workflow_task.task_modifiers.parallel_count > 1 %}
+{%  if 'parallel_count' in workflow_task.task_modifiers and workflow_task.task_modifiers.parallel_count is not none %}
+{%    if workflow_task.task_modifiers.parallel_count > 1 %}
     {% set parallel_indent = 4 %}
     parallel_count = {{workflow_task.task_modifiers.parallel_count}}
     with kfp.dsl.ParallelFor(list(range(parallel_count))) as rank:
+{%    endif %}
 {%  endif %}
 
 {%  filter indent(width=parallel_indent) %}
@@ -81,9 +83,11 @@ def generated_pipeline(
 {%    for env_var_name, env_var_value in workflow_task.task_modifiers.env_variables.items() %}
     {{ task_name }}.add_env_variable(V1EnvVar(name="{{ env_var_name }}", value="{{ env_var_value | string_delimiter_safe }}"))
 {%    endfor %}
-{%    if workflow_task.task_modifiers.parallel_count > 1 %}
+{%    if 'parallel_count' in workflow_task.task_modifiers and workflow_task.task_modifiers.parallel_count is not none %}
+{%      if workflow_task.task_modifiers.parallel_count > 1 %}
     {{ task_name }}.add_env_variable(V1EnvVar(name="NRANKS", value=str(parallel_count)))
     {{ task_name }}.add_env_variable(V1EnvVar(name="RANK", value=str(rank)))
+{%      endif %}
 {%    endif %}
 {%    if workflow_engine == "argo" %}
     {{ task_name }}.add_env_variable(V1EnvVar(
diff --git a/elyra/tests/pipeline/kfp/test_processor_kfp.py b/elyra/tests/pipeline/kfp/test_processor_kfp.py
index 0750a15a2..cdf0598b8 100644
--- a/elyra/tests/pipeline/kfp/test_processor_kfp.py
+++ b/elyra/tests/pipeline/kfp/test_processor_kfp.py
@@ -735,7 +735,7 @@ def test_generate_pipeline_dsl_compile_pipeline_dsl_one_generic_node_pipeline_te
 
     # Verify component definition information (see generic_component_definition_template.jinja2)
     #  - property 'name'
-    assert node_template["name"] == "run-a-file"
+    assert node_template["name"] == sanitize_label_value(op.name)
     #  - property 'implementation.container.command'
     assert node_template["container"]["command"] == ["sh", "-c"]
     #  - property 'implementation.container.args'
@@ -1416,11 +1416,9 @@ def test_generate_pipeline_dsl_compile_pipeline_dsl_generic_components_data_exch
     assert len(compiled_spec["spec"]["templates"]) >= 3
     template_specs = {}
     for node_template in compiled_spec["spec"]["templates"]:
-        if node_template["name"] == compiled_spec["spec"]["entrypoint"] or not node_template["name"].startswith(
-            "run-a-file"
-        ):
+        if node_template["name"] == compiled_spec["spec"]["entrypoint"]:
             continue
-        template_specs[node_template["name"]] = node_template
+        template_specs[sanitize_label_value(node_template["name"])] = node_template
 
     # Iterate through sorted operations and verify that their inputs
     # and outputs are properly represented in their respective template
@@ -1430,10 +1428,8 @@ def test_generate_pipeline_dsl_compile_pipeline_dsl_generic_components_data_exch
         if not op.is_generic:
             # ignore custom nodes
             continue
-        if template_index == 1:
-            template_name = "run-a-file"
-        else:
-            template_name = f"run-a-file-{template_index}"
+        template_name = sanitize_label_value(op.name)
+        template_name = template_name.replace("_", "-") # kubernetes does this replace
         template_index = template_index + 1
         # compare outputs
         if len(op.outputs) > 0: