No you cannot connect the dishwasher directly into the plumbing system. Dishwasher drains always need to connect indirectly to the system or you will get sewer gas coming back up into the dishwasher. In addition, if there is a sewer backup, guess what stuff will be floating in your dishwasher, or flowing out the front. In an island situation, you can either run a separate drain with a stand pipe like for a washer or you can find a drain in a lower room (if available) to tie the dishwasher in upstream of a trap. You always have to tie in on the fixture side of a trap at least 2 times the pipe diameter above the horizontal drain. In addition, its recommended to run the dishwasher hose drain as high up under the counter under the sink, before heading down to the fixture trap. The water lines are easy, just tie into them anywhere and put a valve under the dishwasher to be able to shut it off.