MySQL 8.0

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CREATE TABLE part_linked (
    part_id INT
    , uid INT
    , parent_part_id INT
    , part_linked_order INT
    );
INSERT INTO part_linked(part_id, uid, parent_part_id) VALUES
(1, 72, NULL),
(2, 102, 1),
(4, 104, 2),
(5, 106, 4),
(3, 103, 1),
(4, 105, 3),
(5, 106, 4);

Records: 7  Duplicates: 0  Warnings: 0


WITH RECURSIVE generation AS (
    SELECT part_id
        , uid
        , parent_part_id
    FROM part_linked
    WHERE uid = 72
    
    UNION ALL
    
    SELECT child.part_id
        , child.uid
        , child.parent_part_id
    FROM part_linked child
    JOIN generation g ON g.part_id = child.parent_part_id
    )
SELECT
      case when p_order > 1 then concat(part_id,'_',p_order) else part_id end as part_linked_order
    , part_id
    , uid
    , parent_part_id
FROM (
    SELECT
          generation.part_id
        , generation.uid
        , generation.parent_part_id
        , ROW_NUMBER() OVER (PARTITION BY part_id ORDER BY parent_part_id) p_order
    FROM generation
  ) d
ORDER BY part_linked_order ASC;


part_linked_order
part_id
uid
parent_part_id


1
1
72
null

2
2
102
1

3
3
103
1

4
4
104
2

4_2
4
105
3

5
5
106
4

5_2
5
106
4

5_3
5
106
4

5_4
5
106
4

part_linked_order	part_id	uid	parent_part_id
1	1	72	null
2	2	102	1
3	3	103	1
4	4	104	2
4_2	4	105	3
5	5	106	4
5_2	5	106	4
5_3	5	106	4
5_4	5	106	4