The Extendability of Cayley Graphs Generated by Transposition Trees

Yongde Feng, Yanting Xie, Fengxia Liu and Shoujun Xu
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Yongde Feng: School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou 730000, China
Yanting Xie: School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou 730000, China
Fengxia Liu: College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
Shoujun Xu: School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou 730000, China

Mathematics, 2022, vol. 10, issue 9, 1-8

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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