WP: The Parent Slug

functions.php

// inside functions.php
function the_parent_slug() {
    global $post;
    if ($post->post_parent == 0 && $post->post_parent) return '';
    $post_data = get_post($post->post_parent);
    return $post_data->post_name;
}

// initiate anywhere
<?php echo the_parent_slug(); ?>