Involve: A Journal of Mathematics

  • Involve
  • Volume 6, Number 1 (2013), 25-33.

Properties of generalized derangement graphs

Hannah Jackson, Kathryn Nyman, and Les Reid

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A permutation on n elements is called a k-derangement (kn) 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.

Article information

Involve, Volume 6, Number 1 (2013), 25-33.

Received: 14 September 2011
Revised: 22 May 2012
Accepted: 13 July 2012
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C69: Dominating sets, independent sets, cliques 05A05: Permutations, words, matrices
Secondary: 05C45: Eulerian and Hamiltonian graphs

derangements Eulerian chromatic number maximal clique Cayley graph independent set


Jackson, Hannah; Nyman, Kathryn; Reid, Les. Properties of generalized derangement graphs. Involve 6 (2013), no. 1, 25--33. doi:10.2140/involve.2013.6.25.

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