what the difference between “viktigaste” and “viktigast”

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Viktigast is the indefinite and viktigaste is the definite form.

They can oftenbe used interchangeably if you restructure the sentence a bit.

Katten är viktigast.
Katten är det viktigaste.
The cat is the most important.

Den viktigaste katten.
The most important cat.

Den katt som är viktigast.
The cat that's the most important.

Det är viktigast att sova på natten.
It's most important to sleep at night.

Det viktigaste är att sova på natten.
The most important thing is to sleep at night.

Viktigaste can be used with a subclause like in the following example.
Viktigast wouldn't work here:

Det här är det viktigaste som har hänt idag
This is the most important thing that's happened today.