We present combinatorial algorithms constructing loop-free P-critical edge-bipartite (signed) graphs Δ′, with n ≥ 3 vertices, from pairs (Δ, w), with Δ a positive edge-bipartite graph having n-1 vertices and w a sincere ...

A graph is s-regular if its automorphism group acts regularly on the set of s-arcs. In this study, we classify the connected cubic s-regular graphs of orders 22p and 22p² for each s ≥ 1, and each prime p.

Some collections of submodules of a module defined by certain conditions are studied. A generalization of the notion of radical (preradical) filter is considered. We study the form of filters of semisimple modules and direct sums.

It is proved that if π-Hall subgroup is a supersolvable group then the derived π-length of a π-solvable group G is at most 1 + maxr∈π lαr(G), where lαr(G) is the derived r-length of a π-solvable group G.

We present a brief scientific biography of Professor Petro M. Gudivok.

This article is devoted to the number of non-negative solutions of the linear Diophantine equation a₁t₁ + a₂t₂ + ⋯ + antn = d, where a₁,…,an, and d are positive integers. We obtain a relation between the number of solutions ...