Changing menu settings for custom content type programmatically.

hi, i have added a menu named vt menu with the system's menu proggrammatically. i try to create a custom content type with fields.
i want to change content type's default parent item to vt menu during module installation. i have added my hook_install codes below.

what functions do i need to add along with my hook_install function to achieve this?

here is my vt_tech.install file

function vt_tech_install() {
  node_types_rebuild();
  $types = node_type_get_types();
  
  foreach (_vt_tech_installed_fields() as $field) {
    field_create_field($field);
  }
  
  foreach (_vt_tech_installed_instances() as $instance) {
    $instance['entity_type'] = 'node';
    $instance['bundle'] = 'vt_tech';
    field_create_instance($instance);
  }
  
  variable_set('comment_vt_tech', COMMENT_NODE_CLOSED);
}