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math.CO2025
The automorphism groups and identification of some Generalized Paley Graphs
Ilia Ponomarenko
The family of generalized Paley graphs of prime power order and degree is studied. It is shown that the automorphism group of a graph in this family is a subgroup of…
math.CO2025
A lower bound for the Weisfeiler-Leman dimension of circulant graphs
Yulai Wu, Qing Ren, Ilia Ponomarenko
It is proved that for infinitely many positive integers n, there exists a circulant graph of order n whose Weisfeiler-Leman dimension is at least c\sqrt{log n} for some positive co…
math.CO2023
On the Weisfeiler algorithm of depth- stabilization
Gang Chen, Qing Ren, Ilia Ponomarenko
An origin of the multidimensional Weisfeiler-Leman algorithm goes back to a refinement procedure of deep stabilization, introduced by B. Weisfeiler in a paper included in the colle…