The Extendability of Cayley Graphs Generated by Transposition Trees

The Extendability of Cayley Graphs Generated by Transposition Trees

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 (...

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Veröffentlicht in:Mathematics (Basel) 2022-05, Vol.10 (9), p.1575
Hauptverfasser: Feng, Yongde, Xie, Yanting, Liu, Fengxia, Xu, Shoujun
Format: Artikel
Sprache:eng
Schlagworte:
bubble-sort graphs
cayley graphs
extendability
Graphs
Integers
Matching
Mathematics
star graphs
transposition trees
Trees (mathematics)
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Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10091575