*Article* **The Extendability of Cayley Graphs Generated by Transposition Trees**

**Yongde Feng 1,2, Yanting Xie 1, Fengxia Liu <sup>2</sup> and Shoujun Xu 1,\***


**Abstract:** A connected graph Γ is *k*-extendable for a positive integer *k* if every matching *M* of size *k* can be extended to a perfect matching. The extendability number of Γ is the maximum *k* such that Γ is *k*-extendable. In this paper, we prove that Cayley graphs generated by transposition trees on {1, 2, ... , *n*} are (*n* − 2)-extendable and determine that the extendability number is *n* − 2 for an integer *n* ≥ 3.

**Keywords:** extendability; cayley graphs; transposition trees; bubble-sort graphs; star graphs

**MSC:** 05C25; 05C70
