# 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 | | 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

## 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 | | 3 Comments

## A little problem

In connection with the power graphs of unitary groups, I came across the following little number-theoretic 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

Posted in open problems | | 6 Comments

## 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 | | 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 | | 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

## 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

Posted in mathematics | | 8 Comments

## 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

Posted in open problems | | 3 Comments

## Graphs defined on groups

Apologies; I have been so busy lately that very little has got written up. Let me try to remedy this with a quick tour through some recent mathematical developments. As some of my posts have hinted, one topic I have … Continue reading