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The purpose of this paper is to clarify all of the uniformly relatively Dingstable toric Fano threefolds and fourfolds as well as unstable ones. The keyplayer in our classification result is the Mabuchi constants, which can becalculated by combinatorial data of the associated moment polytopes due to thework of Yao [33]. In Tables 1-3, we give the list of uniform relative Dingstability of all toric Fano manifolds in dimension up to four with the valuesof the Mabuchi constants.  As an application of our main theorem (Theorem 1.1), we clarify thedifference between relative $K$-stability and relative Ding stability byconsidering some specific toric Fano manifolds (Corollaries 1.6 and 1.9). Inthe proof of Corollary 1.9, we used Bott tower structure of relatively Dingunstable toric Fano manifolds.

Relative Ding and $K$-stability of toric Fano manifolds in low dimensions