Most rigid representations and Cayley index
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Date
2018
Authors
Morris, Joy
Tymburski, Josh
Journal Title
Journal ISSN
Volume Title
Publisher
University of Primorska
The Slovenian Discrete and Applied Mathematics Society
The Slovenian Discrete and Applied Mathematics Society
Abstract
For any finite group G, a natural question to ask is the order of the smallest possible automorphism group for a Cayley graph on G. A particular Cayley graph whose automorphism group has this order is referred to as an MRR (Most Rigid Representation), and its Cayley index is a numerical indicator of this value. Study of GRRs showed that with the exception of two infinite families and thirteen individual groups, every group admits a Cayley graph whose MRR is a GRR, so that the Cayley index is 1. The full answer to the question of finding the smallest possible Cayley index for a Cayley graph on a fixed group was almost completed in previous work, but the precise answers for some finite groups and one infinite family of groups were left open. We fill in the remaining gaps to completely answer this question.
Description
Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Cayley graph , Cayley index , GRR , MRR , Automorphisms
Citation
Morris, J. & Tymburki, J. (2018). Most rigid representations and Cayley index. The Art of Discrete and Applied Mathematics, 1, Article #P1.05. https://doi.org/10.26493/2590-9770.1242.809