**4. Conclusions**

Although computing the Khovanov homology of links is common in the literature, no general formulae have been given for all families of knots and links. In this paper, we considered a general three-strand braid *x*1*x*2*x*1*x*2 ··· , which, depending on the powers of Garside element Δ = *x*1*x*2*x*1, is divided into six subclasses, and gave the Khovanov homology of Δ2*k*+1, <sup>Δ</sup>2*k*+1*x*2, and <sup>Δ</sup>2*k*+1*x*1 (To learn more about these classes, see Reference [23–26].) The results particularly cover the 0th, 1st, and top homology groups of these classes, and all homology groups, in general, of link Δ2*k*+1. We hope the results will help classifying links, and in studying the important properties of these links.

**Author Contributions:** Formal analysis, Y.C.K.; writing—original draft, A.R.N., Z.I., D.A., and S.M.K.; writing—review and editing, M.M.

**Funding:** This work was supported by the Dong-A University research fund.

**Acknowledgments:** We are very thankful to the reviewers for their valuable suggestions to improve the quality of this paper.

**Conflicts of Interest:** The authors declare that they have no conflicts of interest.
