2012/04/24 by Peter Hegarty, Hegarty, Peter, Dmitry Zhelezov +1
Computer Science · Engineering · Mathematics · #20P05 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Probability (math.PR) #graph theory and CDMA systems #math.GR #math.PR #msc:20P05
paper · pdf · doi:10.48550/arxiv.1204.5456
12 pages, 2 figures. This is a reworked version of an earlier flawed paper. Previously, the paper contained an erroneous proof of what is now Conjecture 3.4. In this version, we content ourselves with presenting heuristic and numerical evidence in its favour
openalex publication_date 2012/04/24 · arxiv created 2012/08/30 · arxiv updated 2012/08/31 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We present a family of finite, non-abelian groups and propose that there are members of this family whose commuting graphs are connected and of arbitrarily large diameter. If true, this would disprove a conjecture of Iranmanesh and Jafarzadeh. While unable to prove our claim, we present a heuristic argument in favour of it. We also present the results of simulations which yielded explicit examples of groups whose commuting graphs have all possible diameters up to and including 10. Previously, no finite group whose commuting graph had diameter greater than 6 was known.