Vol. 6, No. 1, 2013

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ISSN: 1944-4184 (e-only)
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Properties of generalized derangement graphs

Hannah Jackson, Kathryn Nyman and Les Reid

Vol. 6 (2013), No. 1, 25–33
Abstract

A permutation on n elements is called a k-derangement (k n) if no k-element subset is mapped to itself. One can form the k-derangement graph on the set of all permutations on n elements by connecting two permutations σ and τ if στ1 is a k-derangement. We characterize when such a graph is connected or Eulerian. For  n an odd prime power, we determine the independence, clique and chromatic numbers of the 2-derangement graph.

Keywords
derangements, Eulerian, chromatic number, maximal clique, Cayley graph, independent set
Mathematical Subject Classification 2010
Primary: 05C69, 05A05
Secondary: 05C45
Milestones
Received: 14 September 2011
Revised: 22 May 2012
Accepted: 13 July 2012
Published: 23 June 2013

Communicated by Ann Trenk
Authors
Hannah Jackson
Mathematics Department
Syracuse University
215 Carnegie
Syracuse, NY 13244
United States
Kathryn Nyman
Mathematics Department
Willamette University
900 State Street
Salem, OR 97301
United States
Les Reid
Mathematics Department
Missouri State University
901 South National Avenue
Springfield, MO 65897
United States