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 ...

Let G be a group. An element w(x, y) of the absolutely free group on free generators x, y is called an associative word in G if the equality w(w(g₁, g₂), g₃)=w(g₁, w(g₂, g₃)) holds for all g₁, g₂ ∈ G. In this paper we ...

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.

In this work the closure operators of a category of modules R-Mod are studied. Every closure operator C of R-Mod defines two functions F₁с and F₂с, which in every module M distinguish the set of C-dense submodules F₁с(M) ...

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.

We prove that varieties of (ℓr, rr)-dibands and (ℓn, rn)-dibands coincide and describe the structure of free (ℓr, rr)-dibands. We also show that operations of an idempotent dimonoid with left (right) regular bands coincide, ...

If G is a group with a presentation of the form ⟨x, y|x³ = yq = W(x, y)² = 1⟩, then either G is virtually soluble or G contains a free subgroup of rank 2. This provides additional evidence in favour of a conjecture of Rosenberger.

A convolution is a mapping C of the set Z⁺ of positive integers into the set P(Z⁺) of all subsets of Z⁺ such that every member of C(n) is a divisor of n. If for any n, D(n) is the set of all positive divisors of n, then D ...

The computation of the Möbius function of a Möbius category that arises from a combinatorial inverse semigroup has a distinctive feature. This computation is done on the field of finite posets. In the case of two combinatorial ...

The concept of graph structure was introduced by E. Sampathkumar in 'Generalised Graph Structures', Bull. Kerala Math. Assoc., Vol 3, No.2, Dec 2006, 65-123. Based on the works of Brouwer, Doob and Stewart, R.H. Jeurissen ...