Venting sink in island

My kitchen sink is going to be in an island. My dishwasher will also be in the island, directly to the right of my sink. I think that I need to make a loop vent under the island, with both legs of the loop going under the floor, the drain dying into my drain line & the vent line ending higher than the drain & traveling to where it can go up a wall to the kitchen vent stack. My vent stack will be about 6 feet away I think. I will make sure the slope is sufficient. My question is, how does my DW tie into all this? Do I need to leave sufficient room between the sink & DW for the loop, or I guess I could put it on the left side? Sorry if this makes no sense. I am very much an amatuer trying to find some guidance. Thanks so much!

If the sink is going to have a disposal, use the knockout provided...
If not, ensure you run the drain low enough in the island vent system to include a dishwasher wye tailpiece in your sink drain...
Make sure you either run the DW to an above counter airbreak or at least a high loop before attaching it to the drain...

look for an illistration for a BOW vent that is what you need.