this should be the default behaviour. when you delete a page via site admin, the deletion is replicated to any publish instances reachable via the replication agents configured on author. you can initiate a delete replication also programmatically by using the Replicator service.
When I delete via the site admin, it gets replicated to publishers. When i programatically delete something, the deletion is not being replicated. Can you provide me a code snippet on how to initialte the delete replication programatically? I probably need to do that after deleting the content programatically.