SS EDWARD BURLESON (I don't find the ship listed as EDWARD S. BURLESON) was constructed in 57 days in April-June 1943 by the Todd Houston Shipbuilding Company, Houston, Texas. Her keel was laid April 15, 1943, she was launched May 27, and she was completed and delivered for service on June 11. She likely had an uneventful wartime career since I can find no unusual mentions of her. She was scrapped in Oakland, California, in 1963. See http://www.mariners-l.co.uk/LibShipsE.html and scroll down to the name of the ship. Also see http://shipbuildinghistory.com/history/shipyards/4emergencylarge/wwtwo/toddhouston.htm and scroll to hull number 63. The ship was named after Edward Burleson (1798-1851), a frontiersman, commander at the siege of the Alamo and Vice President of the Republic of Texas.
I found brief online mentions of the ship at http://hellhappiness.wordpress.com/2011/02/17/remembering-my-father-on-deer-lodge-day/ and http://www.armed-guard.com/trip5.html. The latter page also has a number of photographs taken aboard the ship, although there is no indication that the photographs are from a voyage during which your father was aboard.
I will search for additional information about your father and provide what I find in another message. Was your father an Armed Guard or was he a merchant mariner? If the latter, what was your father's position aboard this or any other ship?
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website