APAedan Pope
Aedan Pope
*This is an algorithmically generated author record based on publicly available information.
Research Subjects
Research Interests
Aedan Pope has a total of 1 co-authors. Here are the top co-authors by number of shared publications:
- Michael Giudici
The University of Western Australia
2 shared publications
Latest Publications
- 1 January 2014
- Published by Walter de Gruyter GmbH in Journal of Group Theory
- Vol. 17 (1)
On bounding the diameter of the commuting graph of a group
: The commuting graph of a group
- 1 January 2014
- Published by Walter de Gruyter GmbH in Journal of Group Theory
- Vol. 17 (1)
On bounding the diameter of the commuting graph of a group
: The commuting graph of a group
- Open Access
On Bounding the Diameter of the Commuting Graph of a Group
The commuting graph of a group $G$ is the simple undirected graph whose vertices are the non-central elements of $G$ and two distinct vertices are adjacent if and only if they commute. It is conjectured by Jafarzadeh and Iranmanesh that there is a universal upper bound on the diameter of the commuting graphs of finite groups when the commuting graph is connected. In this paper we determine upper bounds on the diameter of the commuting graph for some classes of groups to rule them out as possible counterexamples to this conjecture. We also give an example of an infinite family of groups with trivial centre and diameter 6, the previously largest known diameter for an infinite family was 5 for $S_n$.Open AccessOn Bounding the Diameter of the Commuting Graph of a Group
The commuting graph of a group $G$ is the simple undirected graph whose vertices are the non-central elements of $G$ and two distinct vertices are adjacent if and only if they commute. It is conjectured by Jafarzadeh and Iranmanesh that there is a universal upper bound on the diameter of the commuting graphs of finite groups when the commuting graph is connected. In this paper we determine upper bounds on the diameter of the commuting graph for some classes of groups to rule them out as possible counterexamples to this conjecture. We also give an example of an infinite family of groups with trivial centre and diameter 6, the previously largest known diameter for an infinite family was 5 for $S_n$.