Cara Gatlin and Vernon Appleton, both of Topeka, have announced their engagement.She is the daughter of Carole Domogala, Phoenix, Ariz., and J. Alan Gatlin, Vista, Calif. He is the son of Diane Appleton, Dodge City, and Kenny Appleton, Dumas, Texas. Her grandparents are Dylce and Louise Dietz, Ottawa, and Mary Lou and the late Nathan Gatlin, Ottawa. His grandparents are Robert and Dorothy Gates and Bessy and the late Vernon Appleton, Buffalo, Okla. They both are graduates of Washburn University. The wedding is scheduled for June at Ward Mead Park in Topeka.