Glue to seal round edges of plywood floor?

Does anyone know what would be safe to seal the edges of the floor to prevent it becoming warped so quickly? Just had the floors of my big welfare hutch replaced. They have never fit properly as the wood supporting the floors does not entirely match up. My hope is that if I seal the edges it might last more than another year. I obviously got them on a bad day. It is a shame the floors are poor quality when the rest of it is so good.

I'd nail down some... argh, I've forgetten what it's called! Edging, cornicing, that sort of thing... I used it over the lino in our playhouse to keep that from moving about.

Nail down edging, then silicone around it to seal it

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Hopefully you can see what I mean in the picture

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oh, brilliant. Thank you!