A 12-year NFL veteran, Graham has made 85.4 percent of his kicks, fifth in league history. Graham played in 16 games for Houston last season, setting a team record for points with 138. He connected on 31 of 38 field goals and set a career high with 28 touchbacks.
Graham has appeared in 155 career regular-season games. He was selected to the Pro Bowl following the 2005 season with Cincinnati after he finished third in the league with a team-record 131 points. He spent eight seasons (2003-09) with the Bengals.
Dawson, the last player left from Cleveland's 1999 expansion team, recently signed as a free agent with San Francisco.