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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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2290036 |
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| _version_ | 1846140624423616512 |
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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. |
| format | Article |
| id | doaj-art-724aeb7c45254881949e7afe16adee4f |
| institution | Kabale University |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| 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 |