Tag Archives: clique number

A new constant?

Posted on 23/05/2021 by Peter Cameron

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 , , | 8 Comments

Graphs on groups, 4

Posted on 18/02/2021 by Peter Cameron

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 →

Posted in open problems | Tagged , , | Leave a comment

The power graph yet again

Posted on 15/03/2016 by Peter Cameron

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 →

Posted in exposition, open problems | Tagged , , , , , , , | 4 Comments

9,21,27,45,81,153,…

Posted on 16/10/2014 by Peter Cameron

This is the sequence of degrees of primitive groups which don’t synchronize a map of rank 3, equivalently graphs with clique number and chromatic number 3 having primitive automorphism groups. You could argue that the sequence should start with 3, … Continue reading →

Posted in doing mathematics, open problems | Tagged , , , , , | 2 Comments