What can graphs and algebraic structures say to each other?

Peter J. Cameron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
7 Downloads (Pure)

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.
Original languageEnglish
Number of pages6
JournalAKCE International Journal of Graphs and Combinatorics
VolumeLatest Articles
Early online date14 Dec 2023
DOIs
Publication statusE-pub ahead of print - 14 Dec 2023

Keywords

  • Graphs
  • Algebraic structures
  • Groups
  • Commuting graph
  • Power graph

Fingerprint

Dive into the research topics of 'What can graphs and algebraic structures say to each other?'. Together they form a unique fingerprint.

Cite this