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Tag Archives: clique number
The enhanced power graph is weakly perfect
Earlier this year, I posed a combinatorial problem, a solution to which would imply that, for any finite group G, the enhanced power graph of G is weakly perfect, that is, has clique number equal to chromatic number. Recall that … Continue reading
Posted in doing mathematics
Tagged chromatic number, clique number, enhanced power graph, Euler's totient
19 Comments
Graphs on groups, 11
A brief interlude to describe another recent preprint, and as in the preceding post I will concentrate on one result in the paper. I don’t know why it happens, but in this project one of the most interesting graph parameters … Continue reading
Posted in doing mathematics, exposition
Tagged clique number, nilpotent group, solubility graph, souble group
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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, 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
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
9,21,27,45,81,153,…
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