Connecting two gigabit switches to a router

Hello.

Currently I have a setup of:

Netvanta 3448 Router
Netvanta 1325T Gigabit Switch.

I have two cat6 cables connecting the switch to the router using link aggregation. I am now going to add a second gigabit switch, an Asante. How can I connect the two gigabit switches so that a computer on switch 1 can transfer to a computer on switch 2 at gigabit speed with the router in the mix? The router is 10/100. If I connect each switch to the router, I will not be able to achieve gigabit transfers between the computers, correct?