What can graphs and algebraic structures say to each other?
Abstract
In the last couple of decades, there has been a big upsurge of research on graphs defined on algebraic structures (groups, rings, vector spaces, semigroups, and others). Much of this has concerned detailed graph-theoretic properties and parameters of these graphs. However, my concern here is to consider how this research can benefit both graph theory and algebra. I am mainly concerned with graphs on groups, and will give three types of interaction between graphs and groups, with examples of each taken from recent research. The paper also contains a number of open questions. This talk was presented at the conference ICRAGAA 2023 held in Thrissur in Kerala, India. I am grateful to the organizers of the conference, and also to Ambat Vijayakumar and Aparna Lakshmanan S, who organized a very productive on-line research discussion on graphs and groups in 2021. Much of what I report has its roots in that discussion. I am grateful to them for organizing this discussion, as well as to the conference organizers, and all my many coauthors.
Citation
Cameron , P J 2023 , ' What can graphs and algebraic structures say to each other? ' , AKCE International Journal of Graphs and Combinatorics , vol. Latest Articles . https://doi.org/10.1080/09728600.2023.2290036
Publication
AKCE International Journal of Graphs and Combinatorics
Status
Peer reviewed
ISSN
0972-8600Type
Journal article
Collections
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