The board search engine doesn't do phrase searches nor does it handle Boolean operators. When I last checked it also didn't do +/- searches. You can try just typing in the name you want in the keyword search box or you can use the surname box (advanced search) box or you can limit your search to the Graham surname board (using the advanced search box) but you can't the more specific type searches on the boards.
I would suggest also searching the Graham mailing list or even ALL mailing lists where you CAN use many Boolean operators and where you can do a "alice graham " exact name search.
http://archiver.rootsweb.ancestry.com/th/index/GRAHAM/Joan