Suborbital graphs of the symmetric group Sn acting on unordered r-element subsets

  • L Nyaga
  • I Kamuti
Keywords: Symmetric group, r‐element subsets, suborbital graphs

Abstract

In this paper we construct the suborbital graphs of the symmetric group Sn acting on unordered r‐element subsets of X = {1, 2, 3, ..., n}, χ(r) (r􀀑,n􀀓 ∈ ℕ) and analyse their properties. It is shown that the suborbital graphs are undirected, connected if 􀀑r􀀑 <½n, and have girth three if n ≥ 3r.

Key words: Symmetric group, r‐element subsets, suborbital graphs

Published
2015-02-10
Section
Articles

Journal Identifiers


eISSN: 1561-7645