## Involve: A Journal of Mathematics

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

### Properties of generalized derangement graphs

#### 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 $στ−1$ 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

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

Dates
Revised: 22 May 2012
Accepted: 13 July 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513733554

Digital Object Identifier
doi:10.2140/involve.2013.6.25

Mathematical Reviews number (MathSciNet)
MR3072747

Zentralblatt MATH identifier
1271.05073

#### Citation

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. https://projecteuclid.org/euclid.involve/1513733554