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ÜLKER, ALPER

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Dr. Öğr. Üyesi

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ÜLKER

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ALPER

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Now showing 1 - 4 of 4
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    PublicationOpen Access
    Exact Sequences of BCK-Modules
    (Fuat Usta, 2022) ÜLKER, ALPER
    BCK-modules were introduced as an action of a BCK-algebra over an Abelian group. Homomorphisms of BCK-modules form an exact sequence which is called BCK-sequence. In this paper, we study homomorphisms of BCK-modules. We show that this homomorphisms have a module structure. Moreover, we show that sequences of Hom functors are BCK-sequences.
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    PublicationRestricted
    Sombor Index of Zero-Divisor Graphs of Commutative Rings
    (Ovidius Univ Press, 2022) Gürsoy, Arif; ÜLKER, ALPER; Kırcali Gürsoy, Necla
    In this paper, we investigate the Sombor index of the zero-divisor graph of DOUBLE-STRUCK CAPITAL Z (n) which is denoted by Gamma(DOUBLE-STRUCK CAPITAL Z (n) ) for n is an element of {p(alpha), pq, p (2) q, pqr} where p, q and r are distinct prime numbers. Moreover, we introduce an algorithm which calculates the Sombor index of Gamma(DOUBLE-STRUCK CAPITAL Z (n) ). Finally, we give Sombor index of product of rings of integers modulo n.
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    PublicationOpen Access
    On the Essential Element Graph of a Lattice
    (Matematikçiler Derneği, 2022) ÜLKER, ALPER
    Let mathcalL be a bounded lattice. The essential element graph of mathcalL is a simple undirected graph varepsilonmathcalL such that the elements x,y of mathcalL form an edge in varepsilonmathcalL, whenever xveey is an essential element of mathcalL. In this paper, we study properties of the essential elements of lattices and essential element graphs. We study the lattices whose zero-divisor graphs and incomparability graphs are isomorphic to its essential element graphs. Moreover, the line essential element graphs are investigated.
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    Independent Domination Polynomial of Zero-Divisor Graphs of Commutative Rings
    (Springer, 2022) Gürsoy, Necla Kırcalı; ÜLKER, ALPER; Gürsoy, Arif
    An independent dominating set of a graph is a vertex subset that is both dominating and independent set in the graph, i.e., a maximal independent set. Also, the independent domination polynomial is an ordinary generating function for the number of independent dominating sets in the graph. In this paper, we examine independent domination polynomials of zero-divisor graphs of the ring Z(n) where n is an element of {2p, p(2), p(alpha), pq, p(2)q, pqr) and their roots. Finally, we prove the log-concavity and unimodality of their independent domination polynomials.