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Browsing Algebra and Discrete Mathematics. - № 2 (26). - 2018 by Issue Date

Browsing Algebra and Discrete Mathematics. - № 2 (26). - 2018 by Issue Date

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  • Connectedness of spheres in Cayley graphs 
    Brieussel, J.; Gournay, A. (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. ...
  • Abelian doppelsemigroups 
    Zhuchok, A.V.; Knauer, K. (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 ...
  • On unicyclic graphs of metric dimension 2 with vertices of degree 4 
    Dudenko, M.; liynyk, B.O. (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 ...
  • Spectral properties of partial automorphisms of a binary rooted tree 
    Kochubinska, E. (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 ...
  • Modules in which every surjective endomorphism has a δ-small kernel 
    Atani, S.E.; Khoramdel, M.; Pishhesar, S.D. (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 ...
  • Endomorphisms of Cayley digraphs of rectangular groups 
    Arworn, S.; Gyurov, B.; Nupo, N.; Panma, S. (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, ...
  • A formula for the number of weak endomorphisms on paths 
    Knauer, U.; Pipattanajinda, N. (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 ...
  • On a graph isomorphic to its intersection graph: self-graphoidal graphs 
    Das, P.K.; Singh, K.R. (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 ...

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