What can graphs and algebraic structures say to each other?

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 cons...

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Main Author: Peter J. Cameron
Format: Article
Language:English
Published: Taylor & Francis Group 2024-09-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
Online Access:https://www.tandfonline.com/doi/10.1080/09728600.2023.2290036
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author Peter J. Cameron
author_facet Peter J. Cameron
author_sort Peter J. Cameron
collection DOAJ
description 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.
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spelling doaj-art-724aeb7c45254881949e7afe16adee4f2024-12-05T07:02:09ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742024-09-0121324925410.1080/09728600.2023.2290036What can graphs and algebraic structures say to each other?Peter J. Cameron0University of St Andrews, St Andrews, UKIn 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.https://www.tandfonline.com/doi/10.1080/09728600.2023.2290036Graphsalgebraic structuresgroupscommuting graphpower graph
spellingShingle Peter J. Cameron
What can graphs and algebraic structures say to each other?
AKCE International Journal of Graphs and Combinatorics
Graphs
algebraic structures
groups
commuting graph
power graph
title What can graphs and algebraic structures say to each other?
title_full What can graphs and algebraic structures say to each other?
title_fullStr What can graphs and algebraic structures say to each other?
title_full_unstemmed What can graphs and algebraic structures say to each other?
title_short What can graphs and algebraic structures say to each other?
title_sort what can graphs and algebraic structures say to each other
topic Graphs
algebraic structures
groups
commuting graph
power graph
url https://www.tandfonline.com/doi/10.1080/09728600.2023.2290036
work_keys_str_mv AT peterjcameron whatcangraphsandalgebraicstructuressaytoeachother