2 citations · 2 across the 5 of their papers we have counts for
6 papers
There is no -regular -irregular graph
Artem Hak, Sergiy Kozerenko, Andrii Serdiuk
A graph is -irregular if its vertices belong to pairwise distinct numbers of triangles. We prove that no -regular -irregular graph exists, settling the last unresolved…
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…
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…
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…
The unitary Cayley graph of upper triangular matrix rings
Waldemar Hołubowski, Sergiy Kozerenko, Bogdana Oliynyk +1
The unitary Cayley graph of a finite unital ring is the simple graph with vertex set in which two elements and are connected by an edge if and only if i…
A note on the triameter of graphs
Artem Hak, Sergiy Kozerenko, Bogdana Oliynyk
In this note, we give answers to three questions from the paper [A. Das, Triameter of graphs, Discuss. Math. Graph Theory, 41 (2021), 601--616]. Namely, we obtain a tight lower bou…