**Table: cat**
    c_id
    c_name
    parent_id

    **Table: page**
    p_id
    page_name
    c_id

DELETE
    FROM cat
    WHERE c_id=x
    AND NOT EXISTS (
    SELECT count( DISTINCT p_id ) as pages
    FROM page
    WHERE c_id =x
    )
    AND NOT EXISTS (
    SELECT count( DISTINCT c_id ) as children
    FROM cat
    WHERE parent_id =x
    );

DELETE c1
FROM cat c1
LEFT JOIN cat c2
  ON c1.c_id = c2.parent_id
LEFT JOIN page p
  ON c1.c_id = p.c_id
WHERE c2.parent_id IS NULL
 AND p.c_id IS NULL
 AND c1.c_id = 1