  In this paper, we show the relation among the relative central extensions in
an isoclinism family of a particular relative central extension of Hom-Lie
algebras. We define the notion of isoclinism on the central relative extensions
of a pair of Hom-Lie algebras. Then, we figure out the concept of isomorphism
in the equivalence class of isoclinisms on the central relative extensions of a
pair of Hom-Lie algebras.
