3 papers
math.CO2026
Transformation Semigroup Perspective on the Magma Monoid
Yakiv Baiduk, Sergiy Kozerenko
The monoid of all binary operations was first introduced by H. S. Kim and J. Neggers in 2008. Since then, different aspects and applications of this monoid were studied, while seve…
math.CO2026
Regular -regular graphs
Artem Hak, Sergiy Kozerenko, Denys Lohvynov +1
We study graphs that are simultaneously regular with respect to the ordinary vertex degree and regular with respect to the triangle degree, that is, the number of triangles contain…
math.CO2025
Regular -irregular graphs
Artem Hak, Sergiy Kozerenko, Andrii Serdiuk
We address the problem proposed by Chartrand, Erdős and Oellermann (1988) about the existence of regular -irregular graphs. We first establish bounds on the -degrees of s…