Digital Repository of Luhansk Taras Shevchenko National University

# Browsing Algebra and Discrete Mathematics. - № 2 (26). - 2018 by Title

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• (ДЗ "ЛНУ імені Тараса Шевченка", 2018)
A weak endomorphisms of a graph is a mapping on the vertex set of the graph which preserves or contracts edges. In this paper we provide a formula to determine the cardinalities of weak endomorphism monoids of finite ...
• (ДЗ"ЛНУ імені Тараса Шевченко", 2018)
A doppelsemigroup is an algebraic system consisting of a set with two binary associative operations satisfying certain identities. Doppelsemigroups are a generalization of semi-groups and they have relationships with such ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2018)
We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded for finitely presented one-ended groups. ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2018)
Let Cay(S, A) denote the Cayley digraph of the semigroup S with respect to the set A, where A is any subset of S. The function f : Cay(S, A) → Cay(S, A) is called an endo-morphism of Cay(S, A) if for each (x, y) ∈ E(Cay(S, ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2018)
Hopfian modules, δ-Hopfian modules. In this paper, we introduce the notion of δ-Hopfian modules. We give some properties of these modules and provide a characterization of semisimple rings in terms of δ-Hopfian modules by ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2018)
Abstract . A graph G is called a graphoidal graph if there exists a graph H and a graphoidal cover ψ of H such that G ∼= Ω(H, ψ). Then the graph G is said to be self-graphoidal if it is isomorphic to one of its graphoidal ...
• (ДЗ"ЛНУ імені Тараса Шевченко", 2018)
We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider ...
• (ДЗ "ЛНУ імені Тараса Шевченка", 2018)
We study asymptotics of the spectral measure of a randomly chosen partial automorphism of a rooted tree. To every partial automorphism x we assign its action matrix Ax. It is shown that the uniform distribution on eigenvalues ...