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