Match statement based on unique relationship properties

Not sure if this is an unusual use case, but not able to find anything in the docs:

My graph has nodes labelled A and B, and relationships between those nodes with property C

I want to return just one A-B relationship per unique property C, for example if there are 4 relationships but only two unique values for C, the MATCH should only return two relationships

I have gotten the list of unique properties with a COLLECT DISTINCT, but I am stuck on the UNWIND.

Here is my current query:

MATCH ()-[x]-()
WITH COLLECT(DISTINCT x.c) AS props
UNWIND props as p
MATCH (a)-[z {c:p}]-(b) RETURN a,b,z LIMIT 1

The LIMIT 1 is returning only one relationship total, not one relationship per prop in p. Am I not understanding how UNWIND translates to a MATCH?

Many thanks,

Phil