Top Posts
Recent comments
 dsp on The enhanced power graph is weakly perfect
 dsp on The enhanced power graph is weakly perfect
 What Lovelace Did: From Bombelli to Bernoulli to Babbage  on Polynomials taking integer values
 What Ada Did: From Bombelli to Bernoulli to Babbage  on Polynomials taking integer values
 Peter Cameron on The enhanced power graph is weakly perfect
Blogroll
 Astronomy Picture of the Day
 Azimuth
 British Combinatorial Committee
 Comfortably numbered
 Diamond Geezer
 Exploring East London
 From hill to sea
 Gödel's lost letter and P=NP
 Gil Kalai
 Jane's London
 Jon Awbrey
 Kourovka Notebook
 LMS blogs page
 Log24
 London Algebra Colloquium
 London Reconnections
 MathBlogging
 Micromath
 Neill Cameron
 neverendingbooks
 Noncommutative geometry
 numericana hall of fame
 Ratio bound
 Robert A. Wilson's blog
 Since it is not …
 Spitalfields life
 Sylvy's mathsy blog
 SymOmega
 Terry Tao
 The Aperiodical
 The De Morgan Journal
 The ICA
 The London column
 The Lumber Room
 The matroid union
 Theorem of the day
 Tim Gowers
 XKCD
Find me on the web

Join 659 other followers
Cameron Counts: RSS feeds
Meta
Tag Archives: commuting graph
Graphs on groups, 10
The lesson of this post and the next in the series is that the most interesting questions (to me, anyway) are not about the girth of the deep commuting graph but instead about the classes of groups G defined by … Continue reading
Posted in doing mathematics, exposition
Tagged 2Engel group, commuting graph, conjugacy, Dedekind group, enhanced power graph, power graph
Leave a comment
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
Posted in events, exposition, open problems
Tagged cograph, commuting graph, nilpotent group, perfect graph, power graph
2 Comments
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
Posted in doing mathematics, mathematics
Tagged commuting graph, enhanced power graph
Leave a comment
Induced subgraphs of power and commuting graphs
For those who like thinking about these things, here is a small observation and a few problems. As I have recently discussed, the power graph of a group is perfect. This means that all its induced subgraphs are perfect, and … Continue reading
Perfectness of the power graph
The power graph of a group is the graph whose vertices are the group elements (sometimes the identity is excluded but it doesn’t matter here), in which x and y are joined if one is a power of the other. … Continue reading
Posted in doing mathematics, exposition
Tagged commuting graph, Lovász, partial preorder, perfect graph, power graph
1 Comment
The power graph yet again
Five years ago, I posted a short update on the power graph of a group. Now, finally, the paper resulting from this has appeared on the arXiv; my coauthors are Ghodratollah Aalipour, Saieed Akbari, Reza Nikandish and Farzad Shaveisi. I … Continue reading