Author Archives: Peter Cameron

About Peter Cameron

I count all the things that need to be counted.

EDI

We hear a lot about equality, diversity and inclusion now. Perhaps it would be good to remind ourselves of the formal definition. A and B are equal if, for all x, we have (x∈A) ↔ (x∈B). A and B are diverse if … Continue reading

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Graphs on groups, 5

I gave two lectures on this stuff to a new research seminar on Groups and Graphs, run by Vijayakumar Ambat in Kochi, Kerala. The first was an introduction to the hierarchy, the second was about cographs and twin reduction, why … Continue reading

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Hoffman, Lovász and Haemers

At the weekend I attended remotely a memorial session for Alan Hoffman, organised by Bill Pulleyblank. I found it informative, as well as moving. Hoffman is well-known in the algebraic graph theory community for a number of remarkable achievements, including … Continue reading

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Three passages

[Dmitri] Egorov [founder of the Moscow School of Mathematics] was a very reserved and modest man, so much so that it would be easy to believe that he lived only for mathematics. […] His publications do not reveal any evidence … Continue reading

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Graphs on groups, 4

Here is a small problem, mixing group theory and number theory, which might appeal to someone. A couple of definitions. The power graph of a group G has an edge from x to y if one is a power of … Continue reading

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Graphs on groups, 3

Since this stuff keeps growing, I have decided to keep the most recent version on the web. It is now nearly twice as long as the first version I circulated. If you are interested, please take a copy: it’s at … Continue reading

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13th Iranian International Group Theory Conference

This week has been rather a rush. As well as the first week of semester (and my first ever experience of on-line undergraduate lecturing), I have been attending the 13th Iranian International Group Theory Conference in Urmia, Iran. (I had … Continue reading

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Graphs on groups, 2

I wrote the long post about this to try to write it out of my system. No luck … I mentioned in that survey that every finite graph is embeddable as induced subgraph in the enhanced power graph, deep commuting … Continue reading

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Cheryl Praeger

Good news for a change. I just heard that Cheryl (my mathematical sister, third most prolific coauthor, and good friend) has been made a Companion of the Order of Australia. https://www.abc.net.au/news/2021-01-26/professor-cheryl-praeger-receives-companion-order-of-australia/13089958 Congratulations Cheryl!

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Graphs defined on groups

I’ve been spending time I can ill afford on various questions related to graphs whose vertex set is a group G and which capture some of the structure of G. (I interpret this to mean that the graph is invariant … Continue reading

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