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Tag Archives: power graph
Graphs on groups, 12
One thing I have learned from the project is that the most interesting question about graphs defined on groups is this: given two types of graph defined on a group G, what is the class of groups for which the … Continue reading
Posted in doing mathematics, exposition
Tagged enhanced power graph, independence graph, power graph, rank, supersoluble group
1 Comment
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
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Graphs on groups, 8
The dark clouds seem to have lifted a bit. Perhaps now, that the last rush of conferences for a while is over, life can return to something like normality … For me the most significant event was the last in … Continue reading
Posted in doing mathematics, events, open problems
Tagged graphs and groups, matching number, power graph
3 Comments
A little problem
In connection with the power graphs of unitary groups, I came across the following little numbertheoretic conundrum. Can anyone solve it? Let q be an odd power of 2 (bigger than 2). Show that (q2−q+1)/3 is not a prime power … Continue reading
A new constant?
This is an appeal for help. Has anyone come across the constant 2.648102…? Here is the background, which connects with my previous posts about graphs on groups. We are interested in the clique number of the power graph of the … Continue reading
Posted in doing mathematics, open problems
Tagged clique number, Euler's function, power graph
8 Comments
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, 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
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