Handler for updating the current site’s last updated date when a published
post is deleted.

function _update_blog_date_on_post_delete( $post_id ) {
	$post = get_post( $post_id );

	$post_type_obj = get_post_type_object( $post->post_type );
	if ( ! $post_type_obj || ! $post_type_obj->public ) {
		return;
	}

	if ( 'publish' !== $post->post_status ) {
		return;
	}

	wpmu_update_blogs_date();
}