Julia Eddington's death certificate (on Ancestry) gives her parents as James F. Graham and Mary C. McCumpsay. I located a Julia Ann Graham age 8 in Jefferson Co., KY in 1880. Her parents were B F and Mary C. There are plenty of family trees on Ancestry for Benjamin Franklin Graham and Mary C. McCumsey. You may want to investigate these and the records they point to.
Or do you have a reason to believe that BF and Mary C. are not Julia's parents?