MariaDB 10.5

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create table mytable (lagr_number varchar(1000), ltran_number varchar(1000));
insert into mytable values 
	('K000001', 'V000001'),
	('K000001', 'V000004'),
	('K000001', 'V000005'),
	('K000002', 'V000001'),
	('K000003', 'V000002'),
	('K000003', 'V000003'),
	('K000004', 'V000005'),
	('K000005', 'V000007'),
	('K000005', 'V000008'),
	('K000006', 'V000009'),
	('K000007', 'V000009');
select * from mytable;


lagr_number
ltran_number


K000001
V000001

K000001
V000004

K000001
V000005

K000002
V000001

K000003
V000002

K000003
V000003

K000004
V000005

K000005
V000007

K000005
V000008

K000006
V000009

K000007
V000009


with recursive 
	edges as (
		select t1.lagr_number as lagr_number1, t2.lagr_number as lagr_number2
		from mytable t1
		inner join mytable t2 on t2.ltran_number = t1.ltran_number
	),
	cte as (
		select lagr_number1, lagr_number2, concat(lagr_number1, ',', lagr_number2) as visited
		from edges
		union all
		select c.lagr_number1, e.lagr_number2, concat(c.visited, ',', e.lagr_number2)
		from cte c
		inner join edges e on e.lagr_number1 = c.lagr_number2
		where not find_in_set(e.lagr_number2, c.visited)
	)
select lagr_number1 as lagr_number, dense_rank() over(order by min(lagr_number2)) as grp
from cte
group by lagr_number1
order by grp, lagr_number1


lagr_number
grp


K000001
1

K000002
1

K000004
1

K000003
2

K000005
3

K000006
4

K000007
4

lagr_number	ltran_number
K000001	V000001
K000001	V000004
K000001	V000005
K000002	V000001
K000003	V000002
K000003	V000003
K000004	V000005
K000005	V000007
K000005	V000008
K000006	V000009
K000007	V000009