The eccentric distance sum (EDS) and degree distance (DD) are two distance-based graph invariants which have been well-studied in recent years. The study on relationships between various graph invariants has received much attention over the past few decades, and some of these research are associated with Graffiti conjectures (Fajtlowicz and Waller, 1987) or AutoGraphiX conjectures (Aouchiche et al., 2006). More recently, several groups of authors have investigated the relationships between several distance-based graph invariants along this line...